Climate Dynamics

, Volume 35, Issue 5, pp 875–886

Response to the eruption of Mount Pinatubo in relation to climate sensitivity in the CMIP3 models

Authors

    • Department of MeteorologyStockholm University
  • Annica M. L. Ekman
    • Department of MeteorologyStockholm University
  • Henning Rodhe
    • Department of MeteorologyStockholm University
Article

DOI: 10.1007/s00382-010-0777-3

Cite this article as:
Bender, F.A., Ekman, A.M.L. & Rodhe, H. Clim Dyn (2010) 35: 875. doi:10.1007/s00382-010-0777-3

Abstract

The radiative flux perturbations and subsequent temperature responses in relation to the eruption of Mount Pinatubo in 1991 are studied in the ten general circulation models incorporated in the Coupled Model Intercomparison Project, phase 3 (CMIP3), that include a parameterization of volcanic aerosol. Models and observations show decreases in global mean temperature of up to 0.5 K, in response to radiative perturbations of up to 10 W m−2, averaged over the tropics. The time scale representing the delay between radiative perturbation and temperature response is determined by the slow ocean response, and is estimated to be centered around 4 months in the models. Although the magniude of the temperature response to a volcanic eruption has previously been used as an indicator of equilibrium climate sensitivity in models, we find these two quantities to be only weakly correlated. This may partly be due to the fact that the size of the volcano-induced radiative perturbation varies among the models. It is found that the magnitude of the modelled radiative perturbation increases with decreasing climate sensitivity, with the exception of one outlying model. Therefore, we scale the temperature perturbation by the radiative perturbation in each model, and use the ratio between the integrated temperature perturbation and the integrated radiative perturbation as a measure of sensitivity to volcanic forcing. This ratio is found to be well correlated with the model climate sensitivity, more sensitive models having a larger ratio. Further, if this correspondence between “volcanic sensitivity” and sensitivity to CO2 forcing is a feature not only among the models, but also of the real climate system, the alleged linear relation can be used to estimate the real climate sensitivity. The observational value of the ratio signifying volcanic sensitivity is hereby estimated to correspond to an equilibrium climate sensitivity, i.e. equilibrium temperature increase due to a doubling of the CO2 concentration, between 1.7 and 4.1 K. Several sources of uncertainty reside in the method applied, and it is pointed out that additional model output, related to ocean heat storage and radiative forcing, could refine the analysis, as could reduced uncertainty in the observational record, of temperature as well as forcing.

Keywords

Volcanic eruptionGCMClimate sensitivity

1 Introduction

In large volcanic eruptions, SO2 and other sulphuric gases can be injected into the stratosphere. Oxidation of these gases produces sulphuric acid, that condenses and forms a sulphuric aerosol haze that can spread to cover the entire globe and remain in the atmosphere for years. The aerosol reflects shortwave radiation from the sun back to space, increasing the planetary albedo and causing a reduction of the surface temperature. To a lesser extent, the aerosol also absorbs terrestrial longwave radiation causing a warming of the stratosphere and a decrease in outgoing longwave radiation.

Compared to anthropogenic and other natural forcings in the climate system, the volcanic radiative forcing acts on a short time scale, making the forcing and the proceeding system response comparatively easy to observe. Since, to first order, the global mean temperature response to a radiative forcing depends on the magnitude rather than other characteristics of the forcing (IPCC 2001; Boer et al. 2007), it is tempting to use the observed effects of volcanic eruptions to estimate how sensitive the climate system may be to other types of forcing, in particular that caused by anthropogenic green-house gases (GHGs).

A measure often used to represent the sensitivity of the climate to radiative forcing is the equilibrium climate sensitivity \((\Updelta T_{2\times {\rm CO_2}}),\) i.e. the change in global mean surface temperature resulting from an instantaneous doubling of the atmospheric CO2 concentration, after the system has reached a new equilibrium. In complex models of the climate system, like coupled atmosphere–ocean general circulation models (AOGCMs), \(\Updelta T_{2\times {\rm CO_2}}\) is an inherent property that can be calculated from perturbation simulations. Due to limited computer resources, \(\Updelta T_{2\times {\rm CO_2}}\) is as a rule estimated using an atmospheric GCM coupled to a mixed-layer ocean, rather than a fully coupled AOGCM. IPCC (2007) reports a range of equilibrium climate sensitivities based on different state-of-the-art GCMs between 2.0 and 4.5 K, with a best estimate of 3.0 K. This range, given as a 66% confidence interval, is often supposed to encompass the sensitivity of the real climate system, but the possibility of values well outside this interval has been put forward by e.g. Stainforth et al. (2005), and as pointed out by e.g. Knutti and Hegerl (2008) it has proved particularly difficult to rule out high values of climate sensitivity. Refining the estimate of climate sensitivity is for many reasons a matter of concern.

The impact of volcanic eruptions on the atmospheric temperature has been diligently studied and documented (e.g. Bradley 1988; Dutton and Christy 1992; Hansen et al. 1992; Robock and Mao 1995; Robock 2000; Soden et al. 2002, and references therein). Several studies have also investigated the relation between the response to the radiative perturbation of large volcanic eruptions and the response to other radiative forcings, possibly linking the volcanic response to climate sensitivity; Lindzen and Giannitsis (1998) showed that, using a simple box model, higher equilibrium climate sensitivity results in a stronger temperature response to volcano-like radiative forcing and a slower return to equilibrium after the perturbation. Wigley et al. (2005a) used a large ensemble of simulations with one GCM and found an even stronger dependence of temperature response to volcanic forcing on climate sensitivity. The results of Yokohata et al. (2005), who used two versions of one GCM, differing in equilibrium climate sensitivity, are qualitatively similar, and show greater response and longer decay time for the higher sensitivity system. Where Wigley et al. (2005a) conclude that an equilibrium climate sensitivity above 4.5 K cannot be ruled out, Yokohata et al. (2005) find their low-sensitivity model \((\Updelta T_{2\times {\rm CO_2}}=4.0\,\hbox{K})\) to be more realistic than their high-sensitivity model \((\Updelta T_{2\times {\rm CO_2}}=6.3\,\hbox{K})\) and Lindzen and Giannitsis (1998) find their results to support the use of sensitivities at the lower end of their studied span, ranging from 0.24 to 4.8 K. Boer et al. (2007) on the other hand, find the temperature response to volcanic forcing in two GCMs with different equilibrium climate sensitivity to be very similar, and conclude that climate sensitivity cannot be inferred from the temperature record, even when the radiative forcing is known, if the change in ocean heat storage is not accurately known. The importance of ocean heat flux is also pointed out by Wigley et al. (2005b), in a critical comment on Douglass and Knox (2005a), who claim to find support for a low climate sensitivity using observations of radiation and temperature anomalies following a volcanic eruption. The same analysis has also been criticized by Robock (2005), and further discussed in Douglass and Knox (2005b, c) and Douglass et al. (2006).

Apparently there is still a lack of consensus on how, if at all, knowledge of temperature and radiative perturbations following a volcanic eruption can be used to draw conclusions about climate sensitivity. The World Climate Research Programme’s (WCRP’s) Coupled Model Intercomparison Project phase 3 (CMIP3) multi-model data set, formerly known as the model simulations performed in support of the IPCC 4th Assessment Report, provides a broad basis for further investigation of these issues. In this framework of complex models we can test several of the previous conclusions reached in studies using simpler models and smaller simulation ensembles. We choose to focus this study on the eruption of Mt. Pinatubo in the Philippines in June 1991, because it is a recent, major, low-latitude eruption, proven by the instrumental record to have global impact.

A few difficulties related to the following analysis must be addressed; first, the radiative forcing due to a volcanic eruption is neither explicitly observed nor calculated in the models, so instead we study time series of the reflected top-of-atmosphere (TOA) solar radiation, available from models as well as satellite observations. This means that any feedbacks affecting the radiative flux will be encompassed, and the applied forcing is not isolated. See further discussion in Sect. 3.4. Second, observations of radiative perturbation and response are not trivial and cannot be assumed to be completely accurate. Even if the signal from a major volcanic eruption is strong, it may be hard to distinguish from natural variability, especially since there is no possibility of multiple realizations of each “volcanic experiment”. This is particularly a problem for ENSO-induced temperature variations, that are of similar magnitude and time scale as the temperature response to large volcanic eruptions. When a volcano erupts during an on-going El Niño event, which is the case for the Mt. Pinatubo eruption, the volcanic signal will be dampened by the positive temperature anomaly caused by the El Niño. Several attempts have been made to remove the ENSO-signal from the temperature record. This is most often done through linear regression of the temperature data on an ENSO index, like the Southern Oscillation Index, including a time lag (Robock and Mao 1995; Kelly and Jones 1996; Wigley 2005; Santer et al. 2001). Angell (2000) uses empirical orthogonal functions and Thompson et al. (2009) use a simple thermodynamic model to calculate the ENSO-driven components of the temperature. The ENSO-induced modultation of the global mean surface temperature data is up the order of ±0.1 K, and here the ENSO-influence on the volcanic signal is accounted for in a simplified way (Sect. 3.7). Third, the Mt. Pinatubo eruption is preceded by the major eruptions of El Chichón (1982) and Agung (1963), and although the radiative perturbations from the previous eruptions have decayed completely the response could possibly still linger in the state of the ocean and the global surface temperature record, contaminating the results (Lindzen and Giannitsis 1998). But since our primary interest is relative perturbation sizes, rather than absolute levels, this should not be a problem in the present analysis.

This paper is outlined as follows. In Sect. 2 we describe the model output and observational data utilized in the analysis. Section 3 presents the results, in order of appearance including the general agreement of modelled and observed radiative perturbation and temperature response (Sect. 3.1), time scales of delay (Sect. 3.2) and relaxation (Sect. 3.3) of the temperature response, relations between radiative perturbation, temperature response and climate sensitivity (Sect. 3.4), effects on clouds and cloud radiative forcing (Sect. 3.5) and ocean heat storage (Sect. 3.6) and finally estimation of climate sensitivity using observations and the model simulations (Sect. 3.7). Here the methods used are described conjoint with the results. Conclusions are given in Sect. 4.

2 Models and observational data

The modelling groups participating in the CMIP3 have performed simulations of the twentieth century climate, including forcing from anthropogenic GHGs, atmospheric aerosols, solar variability, etc. according to available historical data. Of the more than 20 GCMs involved, 12 include volcanic forcing in their simulations of the past-to-present climate. These models, and their ocean components, are listed in Table 1, which also displays the parameterizations describing the distribution of the volcanic aerosol in the simulations, that varies between the models. Further model documentation and references can be found at http://www-pcmdi.llnl.gov/ipcc/model_documentation/ipcc_model_documentation.php.
Table 1

IPCC models including volcanic forcing in their simulations of the twentieth century climate

Model name (ocean model)

Atmospheric resolution

Volcanic parameterization

GFDL CM2.0 (OM3P4)

2.0° × 2.5° L24

SH

GFDL CM2.1 (OM3P4)

2.0° × 2.5° L24

SH

GISS-EH (HYCOM)

4.0° × 5.0° L20

SH

GISS-ER (Russell)

4.0° × 5.0° L20

SH

PCM (POP)

T42 L26

A

MIROC3.2 (medres) (COCO3.3)

T42 L20

SH

MIROC3.2 (hires) (COCO3.3)

T106 L56

SH

INM-CM3.0

4.0° × 5.0° L21

A

UKMO-HadGEM1 (HadGOM1)

N96 L38

SH

CCSM3 (POP 1.4.3)

T85 L26

A

MRI-CGCM2.3.2

T42 L30

Solar const.

ECHO-G (HOPE-G)

T30 L19

Solar const.

Model names, ocean model names (in cases of independent ocean models), atmospheric resolution and type of volcanic parameterization (SH for Sato et al. 1993; Hansen et al. 2002 and A for Ammann et al. 2003) are indicated. The model ensemble comprises two models (GFDL CM2.0 and GFDL CM2.1) developed at the NOAA Geophysical Fluid Dynamics Laboratory, USA, with differing atmospheric dynamical cores, two models (GISS-EH and GISS-ER) from the NASA Goddard Institute for Space Studies, USA, that differ only in their ocean components, two models (PCM and CCSM3) developed at the National Center for Atmospheric Research, USA, two models [MIROC3.2 (medres) and MIROC3.2 (hires)] jointly developed at the University of Tokyo, the National Institute for Environmental Studies, and the Frontier Research Center for Global Change, Japan, with different resolutions, one model (INM-CM3.0) developed at the Institute for Numerical Mathematics, Russia, one model (MRI-CGCM2.3.2) developed at the Meteorological Research Institute, Japan, and one model (ECHO-G) jointly developed by the Meteorological Institute of the University of Bonn and the Meteorological Research Institute of the Korea Meteorological Administration, and Model and Data group, Germany and Korea

The data set that a majority of the models base their volcanic aerosol parameterization on is the zonal mean vertically resolved optical depths at 550 nm, and column average effective radii given by Sato et al. (1993). This data set is complemented to include the Mt. Pinatubo eruption according to Hansen et al. (2002). In the two GFDL-models (GFDL CM2.0 and GFDL CM2.1) the effective radii of the aerosol particles are modified according to Stenchikov et al. (1998). The parameterizations in the two NCAR models (PCM and CCSM3) are based on zonal mean optical depths at 550 nm calculated from modelled transport of the volcanic sulphate released in each eruption, assuming a fixed aerosol size distribution, as described by Ammann et al. (2003). The INM model (INMCM3.0) uses the same parameterization as the NCAR models. Even for models using the same parameterizations of the optical depth at 550 nm the radiative forcing may differ, due to different model assumptions regarding aerosol extinction coefficients.

Following Stenchikov et al. (2006), who study the Arctic Oscillation response to volcanic eruptions in the CMIP3 models, the two models that parameterize the volcanic radiative perturbation through a modification of the solar constant are excluded from further analysis. Stenchikov et al. (2006) also choose to exclude models that only have output from a single simulation, while we include these models [INM-CM3.0, MIROC3.2 (hires) and UKMO HadGEM1] in our analysis. The remaining seven models supply multiple realizations, and by studying the mean of three ensemble members for each of these models we can reduce noise in the output data. We note that including the models with single realizations introduces an additional statistical error in the analysis (see Sect. 3.7).

In this study we focus on the surface air temperature and the reflected shortwave radiation at the top of the atmosphere, which is expected to co-vary with the planetary albedo. All time series are de-seasonalized through subtraction of mean annual cycles, derived from a reference period before the time of the eruption (1985–1990). Data are expressed as anomalies from the reference period mean, and linear trends are removed. The observational data, described below, are treated in the same way.

The Earth Radiation Budget Experiment (ERBE) (Barkstrom 1984; Barkstrom and Smith 1986) supplies observations of tropical (20°S–20°N) TOA radiation at the time of the volcanic eruption. In the present analysis the Edition 3 Rev 1 data set from the Earth Radiation Budget Satellite (ERBS) Nonscanner Wide Field of View is used. These data are corrected for a change in satellite altitude and instrument drift during the measurement period, and agree well with other satellite-based earth radiation budget records (Wong et al. 2006). Since monthly means have been found to create a spurious semi-annual cycle in the data, 36-day averages are used (Wielicki et al. 2002). Further we restrict our use of the ERBE data to between January 1985 and July 1993, since there is a period of missing observations between July 1993 and November 1993, after which a significant offset is introduced, that is not relevant to the present analysis.

For observational temperature record we make use of the ECMWF re-analysis product ERA40 (Uppala et al. 2005). Re-analysis data are the result of model calculations rather than pure observations, but the ERA40 assimilation system includes surface temperature observations with good coverage, making the model-component in the re-analysis less significant, and ERA40 surface temperatures have been found to agree very well with direct observational data for the time period studied (Simmons et al. 2004). Simmons et al. (2004) also show that another reanalysis data set, NCEP/NCAR (Kalnay et al. 1996) agrees less well with observational data, both in absolute values and short-term variability. A reason for this is that the NCEP/NCAR assimliation system does not include surface temperature observations incorporated in the ERA40 system. See further discussion in Sect. 3.7.

3 Results

3.1 Radiative perturbation and temperature response

The anomalies in TOA reflected solar flux are shown in Fig. 1. The curves represent averages between 20°S and 20°N, in order to be comparable to ERBE-data of the same quantity (also shown in Fig. 1), and models and observations show peak anomalies of up to 10 W m−2. The globally averaged peak anomalies in the models are ca. 25% smaller. A difference between models and observations is the temporal extent of the perturbation. The observations show a more abrupt decline than the models and return to pre-eruption levels after only 2 years, when some volcanic aerosol still remains in the atmosphere. This could be due to errors in the observations, or it could possibly be explained by changes in cloud cover seen by the satellite.
https://static-content.springer.com/image/art%3A10.1007%2Fs00382-010-0777-3/MediaObjects/382_2010_777_Fig1_HTML.gif
Fig. 1

Tropical (20°S–20°N) reflected shortwave flux anomalies (with respect to the 1985–1990 mean) at the top of the atmosphere in ten models and ERBE observations (thick solid line). The time series are displayed smoothed with a 3-month running mean

Figure 2 shows the global mean surface temperature anomalies for the same time period. Also shown is observed global mean temperature, given by ERA40 data. Although the models display a general agreement with the observations, the negative temperature anomaly of up to 0.5 K associated with the volcanic eruption is less conspicuous in the observations than in the model ensemble. This discrepancy can partly be explained by the fact that the observational curve is not corrected for ENSO and that the El Niño that occurred in 1991–1992 suppresses the volcanic signal in the observational data. According to Yokohata et al. (2005), whose ENSO-correction is also used in Sect. 3.7, the peak of the negative perturbation should in fact be ca. 0.05 K greater.
https://static-content.springer.com/image/art%3A10.1007%2Fs00382-010-0777-3/MediaObjects/382_2010_777_Fig2_HTML.gif
Fig. 2

Monthly mean, global mean surface temperature anomalies (with respect to the 1985–1990 mean) in ten models and ERA40 (thick solid line). The time series are displayed smoothed with a 3-month running mean

3.2 Delayed temperature response

The surface temperature does not respond immediately to the radiative perturbation. To quantify the time scale for the temperature response to the radiative perturbation we study the correlation between the reflected flux anomalies and the temperature anomalies at different time lags. The correlation is dominated by the volcanic signal and will be negative (since a positive flux anomaly is related to a negative temperature anomaly) and the time lag corresponding to the largest negative correlation indicates the time scale of the delay in the temperature response. Figure 3 shows the variation of the correlation with time lag for the global mean flux and temperature time series, and the time scale can be seen to vary from ca. 2 months [for MIROC3.2 (medres)] to ca. 8 months (for CCSM3). The median time scale for the ten models is 4 months.
https://static-content.springer.com/image/art%3A10.1007%2Fs00382-010-0777-3/MediaObjects/382_2010_777_Fig3_HTML.gif
Fig. 3

Lagged correlations between global mean, monthly mean shortwave flux anomalies and surface temperature anomalies in ten models. The unit of the lag is months, and the correlated time series span from November 1984 to November 1995

As pointed out by Lindzen and Giannitsis (1998) the response is faster over land areas than over ocean areas. Including only land-covered grid points yields a median response time scale of less than one month, with little variation between the ten models. The time scale of the total response is determined by the longer time scale related to the ocean response (median 5 months). The delay time scales suggested here are in fair agreement with those found by Wigley et al. (2005a) but considerably shorter than those found by Lindzen and Giannitsis (1998).

3.3 Relaxation time for temperature perturbation

Due to the large internal variability in the temperature time series it is difficult to objectively determine the relaxation time for the temperature response following the volcanic eruption. As the signal declines it is obscured by noise. This is also recognized by Boer et al. (2007), who suggest averaging times long enough to capture the signal but short enough to avoid averaging over noise when the signal is small. The duration of the perturbation can be crudely estimated as the time from the eruption to the time when the temperature returns to the mean value of the reference period prior to the eruption, to around five years in all models. Consequently, integration times of this order are used in the subsequent analysis. Contrary to Lindzen and Giannitsis (1998); Wigley et al. (2005a) and Yokohata et al. (2005), we find that the models are not easily distinguishable in this respect, and that there is no apparent relation between decay time and model climate sensitivity (as documented by IPCC 2007). Neither does exponential curve fitting, as employed by Wigley et al. (2005a) to quantify the temperature relaxation time, here reveal a relation between decay time and climate sensitivity, but again, the noise in the data makes the fitting uncertain.

3.4 Relation of temperature and radiation perturbations to climate sensitivity

The amplitude of the temperature perturbation following a volcanic eruption has been suggested to be related to the climate sensitivity in a model, more sensitive models giving a larger maximum temperature response (Lindzen and Giannitsis 1998; Harvey and Kaufmann 2002; Wigley et al. 2005a; Yokohata et al. 2005).

Contrary to these results, the models studied here do not display a relation between the magnitude of the maximum temperature perturbation following the volcanic eruption and the documented equilibrium climate sensitivity \((\Updelta T_{2\times {\rm CO_2}}).\) This is partly due to the fact that the temperature signal is noisy, and the peak value may not be representative of the size of the perturbation. The effect of the noise can be reduced by integration of the temperature anomalies in time, and the size of the integrated perturbation does appear to be related to the climate sensitivity in the models. Figure 4 shows the relation between integrated volcano-induced temperature perturbation, i.e. the summed monthly mean surface temperature anomalies during the perturbation, and equilibrium climate sensitivity in the ten models. The same data are also given in Table 2. Although the data display significant scatter there is indication that the size of the temperature perturbation increases with increasing climate sensitivity. The correlation coefficient r is −0.32 if all models are included, but −0.60 (90% significant) if the model INM-CM3.0 is viewed as an outlier.
https://static-content.springer.com/image/art%3A10.1007%2Fs00382-010-0777-3/MediaObjects/382_2010_777_Fig4_HTML.gif
Fig. 4

Integrated globally averaged surface temperature perturbation from June 1991 to June 1996, plotted against equilibrium climate sensitivity in ten models

Table 2

Equilibrium climate sensitivity, integrated temperature perturbation, here globally averaged from June 1991 to June 1996, and the same integrated temperature perturbation scaled by tropically averaged shortwave radiative perturbation integrated from June 1991 to June 1993, representing volcanic sensitivity

Model

\(\Updelta T_{2\times {\rm CO_2}} (\hbox{K})\)

T pert. (K months)

Scaled T pert. (K/W m−2)

GFDL CM2.0

2.9

 −8.4

 −0.086

GFDL CM2.1

3.4

 −6.1

 −0.070

GISS-EH

2.7

 −7.0

 −0.050

GISS-ER

2.7

 −5.4

 −0.045

PCM

2.1

 −6.6

 −0.066

MIROC3.2 (medres)

4.0

 −8.5

 −0.12

MIROC3.2 (hires)

4.3

 −8.9

 −0.11

INM-CM3.0

2.1

 −9.3

 −0.14

UKMO-HadGEM1

4.4

 −8.7

 −0.11

CCSM3

2.7

 −8.3

 −0.10

However, here it may be misleading to compare the sizes of the temperature responses directly since the radiative forcing may not be identical across the models. We therefore have reasons to investigate the forcing in the models a little closer. As mentioned in Sect. 1, the radiative forcing due to the volcanic eruption has a shortwave as well as a longwave component. Since the shortwave forcing is dominating (e.g. Minnis et al. 1993) and particularly, the effect of longwave forcing at the surface is small (Ramachandran et al. 2000), we conclude that the shortwave forcing is a sufficiently good approximation of the total radiative forcing for our purposes. As was also discussed in Sect. 1, lacking model estimates of the actual radiatvie forcing, we must use the shortwave radiative flux perturbation as a proxy for the forcing. This can be justified as the shortwave feedbacks, mainly associated with clouds, can be assumed to be much smaller than the shortwave aerosol forcing. See further discussion in Sect. 3.5.

As was done for the temperature response we integrate the shortwave radiative flux anomalies caused by the volcanic aerosol over time, and find that the integrated shortwave radiation perturbation due to the volcanic aerosol is smaller the more sensitive the model is. Figure 5 shows the sum of the monthly mean TOA flux anomalies during the perturbation, and its relation to equilibrium climate sensitivity in the ten models. The model INM-CM3.0 constitutes an outlying point, and excluding it from the analysis increases the linear correlation coefficient, r, for the relationship from −0.46 to −0.81. The correlation is significant at the 99% level when INM-CM3.0 is excluded and at the 75% level when it is included.
https://static-content.springer.com/image/art%3A10.1007%2Fs00382-010-0777-3/MediaObjects/382_2010_777_Fig5_HTML.gif
Fig. 5

Integrated globally averaged shortwave perturbation from June 1991 to June 1993, plotted against equilibrium climate sensitivity in ten models

These results are consistent with those of Kiehl (2007) who found that the total forcing in the twentieth century is larger in models with smaller climate sensitivity. An explanation for this proportionality could be that the models are tuned to give reasonable temperature responses, regardless of climate sensitivity, to the quite uncertain twentieth century forcing (see e.g. Knutti 2008). However, in the case of the Pinatubo eruption, it is the aerosol optical depth, rather than the radiative forcing or the temperature response that is tuned to observations.

Figure 5 also illustrates the fact that the same aerosol optical depth parameterization can lead to different forcings and radiative perturbations in different models, as mentioned in Sect. 2. Even models that differ only in their ocean components (GISS-ER and GISS-EH) display different values of integrated radiative perturbation, due to internal variability.

3.5 Effects on cloud radiative forcing

The relation of decreasing radiative perturbation with increasing model climate sensitivity remains evident, and appears even stronger when only the clear-sky fluxes in the models are considered. Yet, in the following analysis, we continue using all-sky fluxes since the available clear-sky fluxes from ERBE contain too much missing data for a comparison to be meaningful. Between June 1991 and June 1993 60% of the monthly mean values are missing in the available clear-sky ERBE data.

In the models the clear-sky fluxes can be used to calculate the cloud radiative forcing, as the difference between clear-sky and all-sky fluxes. The magnitude of the negative (i.e. cooling) shortwave cloud radiative forcing is to some extent reduced in all models except INM-CM3.0 at the time of the eruption, indicating that the presence of clouds dampens the perturbation. This may partly be due to cloud feedback, but primarily it is an effect of clouds obscuring or masking the aerosol effect, making the increase in reflection greater in clear-sky regions than in cloudy regions where the reflection is already high. The same is true for e.g. desert regions and other high surface albedo areas (Minnis et al. 1993). The peak magnitude of the tropical mean shortwave cloud radiative forcing anomaly varies between ca. 1.5 and nearly 5 W m−2 in the different models.

Volcanic aerosol has mainly been suggested to influence cirrus clouds, which would be associated primarily with longwave cloud feedback, but even here there seems to be no observational evidence for global scale effects (Luo et al. 2002). Also possible effects on the albedo of deep convective clouds (Minnis et al. 1993) are regionally restricted. Pinatubo-related changes in global mean total cloud cover in all models are small, comparable in size with natural variability. The peak cloud fraction anomalies are of the order of 1% or less, approximately corresponding to changes in shortwave cloud radiative forcing of less than 1 W m−2. The majority of the models show decreases in cloud cover at the time of the eruption, in agreement with the change in cloud radiative forcing, while GISS-EH and GISS-ER show positive anomalies and INM-CM3.0 is the only model with no discernible change in cloud cover. A more detailed analysis of regional effects on different cloud types are beyond the scope of this paper.

3.6 Effects on ocean heat storage

Boer et al. (2007) stress the importance of the ocean heat storage for the model response to the volcanic forcing. The effect of volcanic eruptions on ocean heat content has also been studied in more detail by Church et al. (2005) and Gleckler et al. (2006), and found to be significant, contrary to the calculations of Douglass et al. (2006). Following Raper et al. (2002) we can establish that changes in ocean heat content are driven by changes in the net flux at the ocean surface. Only five models [GFDL-CM2.0, MIROC (medres), MIROC (hires), INM-CM3.0 and UKMO-HadGEM1] supply all necessary surface fluxes for calculating the net ocean surface flux, and they all show a net flux from the ocean to the atmosphere with a peak value of ca 3 W m−2 following the eruption. No systematic model dependence, i.e. no relation to climate sensitivity, can be seen. The change in heat content in the upper 300 m of the ocean (as studied by Church et al. 2005) does not either show a correlation with climate sensitivity. The actual heat flux into the deep ocean can not be calculated from the available model output. Neither are estimates of the mixed layer depth available. Inclusion of these parameters would make useful improvements to future model data bases.

3.7 Inferring climate sensitivity

To scale the temperature perturbation by the radiative perturbation in each model we use the integrated shortwave perturbation over the tropics only (20°S–20°N), to make possible the same scaling procedure with the ERBE data.

The integrated flux perturbation is calculated by summing the monthly mean radiative anomalies during the length of the perturbation and, correspondingly, the temperature anomalies are integrated in time to yield the total negative temperature contribution caused by the eruption. The ratio between the integrated temperature perturbation and the integrated radiative perturbation carries the unit K/W m−2, and may be seen as a measure of the “volcanic sensitivity”, although it is a sensitivity indicating temperature response to integrated tropical shortwave radiative perturbation rather than global average total forcing. (The equilibrium climate sensitivity is measured in K, in response to the given forcing due to doubling of CO2, which is 3.7 W m−2 according to Myhre et al. 1998). Even if this volcanic sensitivity is not a quantitative measure of climate sensitivity it may, as we shall see, fruitfully be used as a relative indicator of climate sensitivity in different systems.

Figure 6 graphically displays the relation between the ratio between the integrated temperature perturbation and the integrated radiative perturbation and the equilibrium climate sensitivity, \(\Updelta T_{2\times {\rm CO_2}},\) of the ten models. The temporal durations of the perturbations are not well defined, and the relation is somewhat dependent on the length of the integration time, for the radiative perturbation as well as the temperature perturbation. Varying the former between 2 and 4 years and the latter between 4 and 6 years yields values of r between −0.70 and −0.83 (95% significant), if we allow for exclusion of the outlying model INM-CM3.0. Including INM-CM3.0 gives correlation coefficients below −0.4. Displayed in Fig. 6 are ratios based on integration of radiative anomalies for two years and temperature anomalies for four years, yielding a seemingly linear relation, with a correlation coefficient of −0.80, excluding INM-CM3.0. Table 2 displays ratios based on integration of radiative anomalies for 2 years and temperature anomalies for 5 years, with a correlation coefficient of −0.76, excluding INM-CM3.0.
https://static-content.springer.com/image/art%3A10.1007%2Fs00382-010-0777-3/MediaObjects/382_2010_777_Fig6_HTML.gif
Fig. 6

Ratio between integrated surface temperature anomaly (global mean from June 1991 to June 1995) and integrated TOA shortwave radiative anomaly (averaged between 20°S and 20°N from June 1991 to June 1993), plotted against equilibrium climate sensitivity in ten models. The dashed line indicates the best fit line to these data, excluding the outlier INM-CM3.0. Extrapolated the line approximately intersects the origin, in accordance with Eq. 2. The horizontal dotted lines indicate the range of observational ratios

Hence, despite variations in formulations and various model properties there seems to be an agreement among models that high sensitivity to doubling of CO2 is associated with high sensitivity to the radiative perturbation imposed by the volcanic eruption. The relation between climate sensitivity and volcanic sensitivity shows far less scatter than the relations between climate sensitivity and temperature perturbation and radiative perturbation respectively.

Considering a simple global energy balance equation, a temperature perturbation, \(\Updelta T,\) caused by a radiative forcing can under certain assumptions be expressed as a function of the forcing, \(\Updelta Q,\) the heat flux into the ocean, \(\Updelta F,\) the radiative forcing due to doubling of \(\hbox{CO}_2, \Updelta Q_{2\times {\rm CO_2}}\) and the equilibrium climate sensitivity, \(\Updelta T_ {2\times {\rm CO_2}}\) (see e.g. Raper et al. 2002; Kiehl 2007 for more detail) as
$$ \Updelta T = \frac{\Updelta Q - \Updelta F}{\Updelta Q_{2\times {\rm CO_2}}}{\Updelta T_ {2\times {\rm CO_2}}}. $$
(1)
Dividing through by \(\Updelta P,\) the integrated shortwave perturbation over the tropics caused by the eruption of Mt Pinatubo yields
$$ \frac{\Updelta T}{\Updelta P}= \left ( \frac{\Updelta Q - \Updelta F}{\Updelta Q_{2\times {\rm CO_2}} \Updelta P} \right ) {\Updelta T_ {2\times {\rm CO_2}}}, $$
(2)
which describes a relationship between the ratio we call the volcanic sensitivity and the equilibrium climate sensitivity. For a linear relation, as indicated in Fig. 6, to emerge, the expression in the brackets on the right hand side must be constant between models. Given the terms included, this is not unreasonable. We can assume that \(\Updelta Q_{2\times {\rm CO_2}}\) is approximately constant, and that the quantity \(\Updelta P\) is related to the true forcing in such a way that the ratio \(\frac{\Updelta Q}{\Updelta P}\) is relatively constant across models. We also find that in the models where \(\Updelta F\) can be calculated (excluding INM-CM3.0) the ratio between \(\Updelta F\) and \(\Updelta P\) varies little (within 5% of the mean value), which is reasonable as the flux into the ocean should to first order depend on the magnitude of the imposed forcing.

We stress that the relationship found between climate sensitivity and volcanic sensitivity is based on the model results exemplified in Fig. 6, but according to Eq. 2 there seems to be support for this empirical finding. This could be further tested if the true forcing and the ocean heat flux or change in ocean heat storage were accurately known for all models.

The major assumption leading to Eq. 1 is that the feedback term is the same for equilibrium feedback as it is for transient forcing and response. Although this is not necessarily true (see e.g Williams et al. 2008) the assumption is apparently sufficiently good to give the approximate linear relation of Fig. 6. We also stress that no assumptions have been made regarding ocean heat storage.

The high correlation found gives us reason to believe that the volcanic sensitivity defined can indeed be used to get an idea of a model’s climate sensitivity through linear regression, as indicated by the line of best fit to the data in Fig. 6. Extending this line of argument, we can use observed radiative flux and temperature data to yield an observational value of the volcanic sensitivity, and link it to an estimate of climate sensitivity. We treat ERBE and ERA40 data in a similar way as the model data, varying the integration time of the ERBE radiative anomalies from 18 months to 2 years and the ERA40 temperature anomalies from 4 to 6 years, which gives a range of observationally based ratios between −0.047 and −0.073 K/W m−2, with a mean value of −0.06 K/W m−2. To take into account the spread resulting from the uncertainty in integration time in the model data we calculate a set of different best-fit straight lines corresponding to varying integration times for shortwave perturbation and temperature response. Using the alleged linear relationship, for each of these regression lines, the span of observational ratios corresponds to values of the equilibrium climate sensitivity of the climate system between 1.7 and 3.2 K, mean and median coinciding at 2.4 K.

As previously mentioned, the ERA40 volcanic temperature anomalies may be somewhat reduced due to ENSO-induced warming. According to Fig. 1 of Yokohata et al. (2005), who use the method of Santer et al. (2001) to correct their surface temperature time series for ENSO variation, the integrated temperature perturbation due to the Mt. Pinatubo eruption is ca. 10% greater when the ENSO-signal is removed. Repeating the above described regression procedure with an integrated temperature perturbation corrected by this factor yields slightly larger estimated values of \(\Updelta T_{2\times {\rm CO_2}};\) varying between 1.9 and 3.5 K, mean and median coinciding at 2.7 K. This is of course a crude way to account for the ENSO variation but we let it suffice, and note that the shift in the estimated climate sensitivity is small compared to the given uncertainty range.

The estimated ENSO correction is also small in comparison with the effect of replacing the ERA40 data with NCAR/NCEP reanalysis data. The NCAR/NCEP temperature anomaly exceeds that of ERA40, resulting in a shift in the estimates of \(\Updelta T_{2\times {\rm CO_2}}\) by ca 1 K, to 3.4 K (or 3.8 K with ENSO-correction). The use of NCAR/NCEP also broadens the uncertainty range by ca 0.5 K. As stated in Sect. 2, we consider the ERA40 data as more trustworthy, being closer to observational data, but we note that this uncertainty could be reduced with less ambiguity in the observational data.

There are also uncertainties associated with the method used. The supposed linear relation between the volcanic sensitivity and climate sensitivity is approximative, and the regression is based on a relatively small range of ratio values using only nine model data points, that are particularly sparse at the end of the interval where the observational sensitivities are found. The statistical error could be reduced if all models had multiple realizations. We find that using the same method but treating each model realization separately decreases the correlation and broadens the inferred span of climate sensitivities to 2.7 ± 1.0 K. The span of inferred climate sensitivities is also broadened when the uncertainty in the slope of the regression lines is taken into account. Substituting values bounded by a 95% confidence interval around the slope gives a range of climate sensitivity estimates between 1.7 and 4.1 K. Last, but not least, the proceeding is dependent on the assumption that the relation between volcanic sensitivity and equilibrium climate sensitivity found in the models is valid also for the real climate system. If the relation seen would prove to be merely a model artifact, the method would disqualify as a way to estimate real climate sensitivity.

Finally, we note that the equilibrium climate sensitivity through its definition is an abstract characteristic of the real climate system. The transient climate sensitivity, defined as the temperature change at the time of CO2 doubling, at an increase rate of 1% per year, may therefore be considered a more meaningful measure. When repeating the described procedure, only replacing equilibrium climate sensitivity with transient climate sensitivity, we find weaker correlations (between −0.55 and −0.71) with the volcanic sensitivity. The regression yields estimates of the transient climate sensitivity between 0.8 and 2.3 K, which may be compared with the range from 1.2 to 2.6 K given by IPCC (2007).

4 Discussion and conclusions

In the ten CMIP3 models that include parameterizations of volcanic aerosol the top-of-atmosphere shortwave radiative flux perturbations and subsequent temperature responses in relation to the 1991 Mt. Pinatubo eruption show a general agreement with data, although in the models, the radiative perturbation is more persistent than ERBE observations show, and the temperature perturbation is somewhat larger than in non-ENSO corrected ERA40 data.

The time scale signifying the delay time between the radiative perturbation and the temperature response is found to be centered around 4 months in the ten models. The time scale is determined primarily by the thermal inertia of the oceans. The temperature response to the radiative perturbation over land is delayed by less than one month.

The general characteristics of radiative and temperature responses to the volcanic eruption are consistent among the models and there is no clear distinction in behaviour between models using different parameterizations of volcanic aerosol.

Closer examination of the radiative flux perturbation singles out one model in the ensemble as an outlier. The reason for the deviating behaviour of this model is an issue that remains to be resolved. With the exception of this one outlying model a relation between the radiative flux perturbation and equilibrium climate sensitivity is made evident, more sensitive models displaying a smaller radiative perturbation. This relation is valid for peak values as well as integrated flux anomalies, and for clear-sky as well as all-sky fluxes.

The relation between radiative perturbation and climate sensitivity affects the relation between temperature perturbation and climate sensitivity. Whereas temperature perturbation has previously been used as an indicator of climate sensitivity, we find it appropriate to first scale it by the radiative perturbation in each model. The ratio between integrated globally averaged temperature perturbation and integrated tropically averaged flux perturbation in the models is strongly correlated with climate sensitivity, more sensitive models displaying a larger ratio. In other words, the more sensitive a model is to the forcing due to doubling of CO2, the more sensitive it is to the forcing caused by the volcanic eruption. Contrary to Boer et al. (2007) we find the relation to be evident independently of estimates of changes in ocean heat content.

If it is assumed that the sensitivity to CO2 forcing and sensitivity to volcanic forcing are related in a similar way in the real climate system we can make use of an observationally based ratio between temperature perturbation and shortwave flux perturbation and find a corresponding “observational” equilibrium climate sensitivity through linear regression. The resulting estimate of the equilibrium climate sensitivity is centered around 2.4 K, or 2.7 K, if ENSO-effects are accounted for, which is in line with, but somewhat lower than, the best estimate of 3.0 K given by IPCC (2007). The uncertainty range found (1.7–4.1 K) is also similar to the 66% confidence interval given by IPCC (2007) (2.0–4.5 K) but its inconsistency with more extreme estimates (as summarized e.g. by IPCC 2007), especially very high values, to some extent indicates a restriction of previous estimates of climate sensitivity.

Shortcomings and uncertainties in the observational data, of temperature as well as radiation, contribute to the uncertainty in the results presented. The present analysis also points at areas of insufficient model data availability, where useful improvements could be made. Consequently, it is recommended that parameters related to ocean heat storage and radiative forcing are included in future model intercomparison data bases.

Acknowledgments

The authors belong to the Bert Bolin Centre for Climate Research. We acknowledge the modeling groups, the Program for Climate Model Diagnosis and Intercomparison (PCMDI) and the World Climate Research Programme’s (WCRP’s) Working Group on Coupled Modelling (WGCM) for their roles in making available the WCRP CMIP3 multi-model dataset. Support of this dataset is provided by the Office of Science, US Department of Energy. We also acknowledge the ECMWF for providing the ERA-40 data through their data server and the NASA Langley Research Center Atmospheric Science Data Center for providing the ERBE data. We thank Lennart Bengtsson, Erland Källén, Johan Nilsson and Johannes Karlsson for valuable discussion.

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© Springer-Verlag 2010