The Effect of Climate Sensitivity on the Response to Volcanic Forcing
T.M.L. Wigley1, C.M. Ammann1, B.D. Santer2 and S.C.B. Raper3
Submitted to Journal of Climate, May 17, 2004
1 National Center for Atmospheric Research. P.O. Box 3000, Boulder, CO 80307
2 PCMDI, Lawrence Livermore National Laboratory, Livermore, CA 94550
3 Climatic Research Unit, University of East Anglia, Norwich NR4 7Tj, U.K. and Alfred Wegener Institute for Polar and Marine research, D-27515 Bremerhaven, Germany
The Effect of Climate Sensitivity on the Response to Volcanic Forcing
T.M.L. Wigley1, C.M. Ammann1, B.D. Santer2 and S.C.B. Raper3
1 National Center for Atmospheric Research. P.O. Box 3000, Boulder, CO 80307
2 PCMDI, Lawrence Livermore National Laboratory, Livermore, CA 94550
3 Climatic Research Unit, University of East Anglia, Norwich NR4 7Tj, U.K. and Alfred Wegener Institute for Polar and Marine research, D-27515 Bremerhaven, Germany,
ABSTRACT
The results from 16 AOGCM simulations are used to reduce internally-generated noise and obtain an improved estimate of the underlying response of 20th century global-mean temperature response to volcanic forcing. An upwelling-diffusion energy balance model (UD EBM) with the same forcing and the same climate sensitivity as the AOGCM is then used to emulate the AOGCM results. The UD EBM and AOGCM results are in excellent agreement, justifying the use of the UD EBM to determine the volcanic response for different climate sensitivities. The maximum cooling for any given eruption is shown to depend approximately on the climate sensitivity raised to power 0.37. After the maximum cooling, for low-latitude eruptions, the temperature relaxes back towards the initial state with an e-folding time of 29–43 months for sensitivities of 1–4oC. Comparisons of observed and modeled coolings after the eruptions of Agung, El Chichon and Pinatubo give implied climate sensitivities that are consistent with the IPCC range of 1.5–4.5oC equilibrium warming for 2xCO2. The cooling associated with Pinatubo appears to require a sensitivity above the IPCC lower bound of 1.5oC, and none of the observed eruption responses rules out a sensitivity above 4.5oC.
1. Introduction
An important aspect of the validation of climate models is to compare their responses to estimates of past forcing with observed changes in climate. Such comparisons may use observed responses to individual forcing events (such as volcanic eruptions) or, on longer time scales, observed changes over the past 20–100+ years in response to a full suite of natural and anthropogenic forcings.
For the latter type of analysis, comparison methods based on regression techniques may yield probabilistic information about the climate sensitivity (T2x), well recognized as a primary source of uncertainty in climate simulations (Mitchell et al., 2001; Allen et al., 2004). Unfortunately, because of the noise of internally-generated variability (in both model simulations and observations) and because of substantial uncertainties in the past forcing history (arising primarily from anthropogenic aerosol forcing uncertainties), regression-based estimates of see and the short time interval spanned by the event minimizes the effects of other forcings and their uncertainties. are highly uncertain – and such estimates do little to narrow the uncertainty bounds defined by other methods. For example, if the applied forcing underestimated the true magnitude of sulfate aerosol-induced cooling over the 20th century, the implied value of T2x would be too low. Spatial pattern information allows us to define joint probability density functions for aerosol forcing and climate sensitivity, but, until aerosol forcing uncertainties can be reduced independently, these analyses still leave large uncertainties for T2x.
An alternative that has been suggested is to use comparisons between the modeled and observed effects of volcanic eruptions for model validation and estimation of the climate sensitivity (Hansen et al., 1993; Lindzen and Giannitsis, 1998). There are three difficulties with this approach, well articulated by Lindzen and Giannitsis (1998; LG98 below). First, even for the eruption of Mt Pinatubo (June, 1991) where satellite data have allowed us to define the forcing with reasonable accuracy, there are still differences between different estimates of the forcing (see, e.g., Santer et al., 2001). Uncertainties in the forcings for earlier eruptions are necessarily larger. Model-based signals therefore have considerable intrinsic uncertainty. Second, there is a signal-to-noise ratio problem. Since the relevant response is on a monthly timescale, and since the response to an individual eruption decays to a negligible amount after only of order 5 years, the noise of internally-generated variability makes it difficult to define the response signal in the observations (although some of these noise influences, such as the effects of ENSO variability, may be removed by empirical methods; see, e.g., Wigley, 2000). Third, short timescale events (spanning 5 years or less) are less sensitive to T2x than longer time scale processes. If the response is relatively insensitive to T2x, then it becomes much more difficult to back out information about T2x from any model/observed data comparison.
LG98 note that the longer time scale response to multiple consecutive eruptions is more strongly dependent on T2x (as pointed out and quantified earlier by Wigley, 1991), so this may provide an alternative way to obtain information on T2x from the observational record. Unfortunately, this approach is confounded by the effects of and uncertainties in other forcings, both natural and anthropogenic.
LG98 attempted to estimate T2x from the global-mean temperature response to volcanic forcings using a three-box, energy-balance climate model with a limited-depth (400m) diffusive ocean. The authors show that this very simple model emulates the results of a slightly more realistic upwelling-diffusion energy-balance model (UD EBM – Hoffert et al., 1981), but the LG98 model still has admitted shortcomings. In this paper we use a more detailed UD EBM to investigate the effect of T2x on the response to 20th century volcanic forcings. In order to determine the credibility of the UD EBM in this context, we compare its results to those obtained using a fully-coupled Atmosphere/Ocean General Circulation Model (AOGCM). The climate sensitivity of the AOGCM is fixed by the model’s physics and parameterizations. The simpler model, however, has a user-specified climate sensitivity. Thus, provided the simpler model is able to match the results of the AOGCM when its sensitivity is set equal to that of the AOGCM, the simpler model may be run for a range of climate sensitivities to see how various characteristics of the response to volcanic forcing vary as the sensitivity is changed.
2. Analytical Results
Some important insights into the influence that climate sensitivity has on the response to volcanic forcing can be gained by solving a simple one-box climate model. The simplest possible model for the effect of external forcing on global-mean temperature is represented by the equation
C dT/dt + T/S = Q(t)
where C is a heat capacity term, Q(t) is the applied external forcing, S (replacing T2x for simplicity) is the climate sensitivity (i.e., the equilibrium temperature change for unit radiative forcing), and T(t) is the change in global-mean temperature. T(t) must be a function of C and S, and we can show that the relative importance of these two terms depends on the characteristic time scale for Q(t).
To do this, suppose that Q(t) is sinusoidal, Q(t) = A sin(t). The solution is then
T(t) = [()2/(1+()2)] exp(-t/) + [S/(1+()2)][A{sin(t) – t cos(t)}]
where is a characteristic time scale for the system, = SC. (Note that the sine/cosine term can be written in the form sin(t+), showing that the asymptotic response follows the forcing with a lag, , but the expanded form is more convenient here.)
We now consider two end-member cases, for high-frequency and low-frequency forcing. For the latter ( < 1/), the asymptotic solution is simply the equilibrium response
T(t) = S A sin(t)
showing no appreciable lag between forcing and response, with the response being linearly dependent on the climate sensitivity and independent of the system’s heat capacity. For the high-frequency case ( > 1/) the solution is
T(t) = [A/(C)] sin(t – /2)
showing a quarter cycle lag of response behind forcing, with the response being independent of the climate sensitivity.
The critical question then is, what is the appropriate time scale for volcanic forcing relative to the characteristic time scale () for the climate system? If representative values are used for C and S (T2x), and a realistic volcanic forcing time scale corresponding to = 1 to 3 radians per year is assumed, then we can show that the response to volcanic forcing should have a relatively small, but non-negligible dependence on the climate sensitivity. This is in accord with model simulation results obtained by Wigley (1991) and by LG981.
1 For a more general analytical treatment in the frequency domain accounting for ocean mixing as an upwelling-diffusion process, see Wigley and Raper (1991). The results are qualitatively the same as derived here.
3. Defining the volcanic response signal
We begin by defining the response to 20th century volcanic forcing based on simulations with a fully coupled AOGCM, the NCAR/USDOE Parallel Climate Model (PCM; Washington et al., 2000). We use results from simulations carried out by Ammann et al. (2003, 2004), which employ a new forcing history developed by Ammann. In total, there are 16 simulations that include volcanic forcing, comprising four-member ensembles for 4 experiments with: Volcanic forcing alone (V); Volcanic plus Solar forcing (VS); Volcanic plus Solar plus Ozone forcing (VSO); and combined Volcanic, Solar, Ozone, well-mixed Greenhouse gases and direct sulfate Aerosol forcing (VSOGA = ‘ALL’). In addition we have 4 short unforced control-run experiments spanning the same interval.
An estimate of the volcanic response signal can be obtained simply by averaging the 4 members of the V ensemble. This ensemble averaging reduces the noise about the volcanic response signal by a factor of about two. To be more specific, for the control runs (which, like all of the simulations, are drift-corrected – see below), the inter-annual standard deviation over 1890–1999, averaged over 4 ensemble members, is 0.171oC. This provides an estimate of the AOGCM’s internally-generated variability that is superimposed on the volcanically-induced temperature signal in any single simulation. Averaging 4 simulations should reduce this noise to about 0.086oC.
We can obtain an independent estimate of the background variability by using the MAGICC climate model (see below) to estimate the ‘pure’ signal (as shown in Fig. 2), subtracting this signal from each of the 4 AOGCM volcano-only (V) runs, and then calculating the standard deviation of the residuals. The mean of this standard deviation is 0.173oC, consistent with the ‘raw’ control-run variability and providing a useful check on the accuracy of the MAGICC signal estimate. After ensemble averaging over the 4 volcano-only runs, the residual variability about the estimated ‘pure’ signal is reduced to 0.090oC, very close to the theoretical value of 0.173/2 = 0.086oC.
A further reduction in the noise is possible by making use of the other runs that include volcanic forcing. For these cases, results for companion experiments to VS, VSO and ALL are available (see Wigley et al., 2004), and these may be subtracted from the ‘with-volcanic-forcing’ cases to give residual volcano-only results (e.g., Vresid = VS – S, where S is a solar-forcing-alone ensemble, etc.) The gain here is less than might naively be expected because, by virtue of their construction method, the residual volcanic cases have amplified noise, which partly offsets the noise reduction that arises from the increase in sample size. When all 16 volcano runs (i.e., four from V, and four each from VS – V, VSO – SO, and ALL – SOGA) are averaged the residual variability reduces to 0.059oC. The reduction in noise compared with what would be obtained from a single AOGCM realization is 65%.
A potentially more important consideration in defining the volcanic signal is the problem of spatial drift in the AOGCM, which is considerable at the hemispheric-mean scale; a warming of 0.156oC/century in the SH and a cooling of 0.167oC/century in the NH. These trends are common to all simulations (see Wigley et al., 2003). We consider only global-mean changes here, however, for which the PCM’s drift is small (–0.011oC/century). Nevertheless, drift effects are removed in all the data we consider.
The resulting time series, consisting of the averaged volcanic signal plus reduced noise, is compared with the results for a single realization in Fig. 1. A characteristic signature for the response to an individual eruption is clearly seen for Santa Maria, Agung, El Chichon and Pinatubo: a rapid cooling over the first 7–18 months, followed by an approximately exponential relaxation back to the initial state. The relaxation time will be discussed further below. Comparing the two panels of Fig. 1 shows how averaging over multiple realizations leads to a much more well-defined volcano-response signature than can be seen in any individual volcano-response experiment. The individual response case corresponds to the real world where we also have only a single realization, so the top panel graphically illustrates the signal-to-noise ratio problem alluded to earlier.
4. Validating the UD model
We now compare the AOGCM results with results obtained using a simple upwelling-diffusion energy balance model (UD EBM), viz. the MAGICC2 model used in various IPCC reports (Wigley and Raper, 1992, 2001; Raper et al., 1996). As part of the IPCC Third Assessment Report (TAR), MAGICC was calibrated by one of the present authors (Raper) against different AOGCMs using the 1% compound CO2 increase experiments coordinated under CMIP (Covey et al., 2003); see Raper et al. (2001) and the Appendix in Cubasch and Meehl (2001). PCM was one of those models, so we use the TAR calibration results to define the model parameters in MAGICC. The parameters are the climate sensitivity, the land-ocean sensitivity ratio, the oceanic mixed-layer depth, the ocean’s effective vertical diffusivity, the rate of change of upwelling rate as a function of temperature, and land-ocean and inter-hemispheric heat exchange rates (note that MAGICC separates the globe into land and ocean ‘boxes’ in each hemisphere). Applying these long time scale calibration results to the much shorter time scales of a volcanic eruption is quite a severe test of the UD EBM.
There is, still, one unspecified parameter. The primary forcing from the AOGCM simulations is produced as optical depth (OD) changes (defined at some specified frequency), while the UD EBM requires input as forcing at the top of the troposphere (in W m-2). The conversion factor between these two is uncertain. Work at the Goddard Institute for Space Studies illustrates this uncertainty. In their early work (Lacis et al., 1992) the conversion for OD at 0.55m (for small
-
2Model for the Assessment of Greenhouse-gas Induced Climate Change
forcings) is 30 W m-2, in Hansen et al. (1997) it is 27 W m-2, while in Hansen et al. (2002) it is 21 W m-2. Results from PCM suggest a value slightly less than the Hansen et al. (2002) value. We chose a value of 20 W m-2 as a somewhat arbitrary estimate, and it is these results that are shown here. Slightly better results might be obtained by ‘tuning’ this value.
Another difference between the AOGCM and UD EBM experiments is in the nature of the input forcing. In the AOGCM, the ‘forcing’ is specified month by month as zonal-mean loading patterns of stratospheric aerosol (Ammann et al., 2003). In the UD EBM, it is only hemispheric-mean forcings that are specified, but the input is still on a monthly time scale.
Figure 2 compares the PCM results (as shown in Fig. 1b) with the MAGICC results. The very close agreement justifies our use of MAGICC (with different climate sensitivities) to obtain reliable estimates of how the volcanic response varies with sensitivity with some confidence3.
3 Note that we have already used the MAGICC simulation in Fig. 2 as the ‘true’ signal to determine the residual variability about the volcanic signal in the PCM results. The similarity between this residual variability and control-run variability provided another test of the MAGICC results.
5. Effect of different climate sensitivities
Figure 3 shows MAGICC results for climate sensitivities of 1.0oC, 2.0oC and 4.0oC (expressing the sensitivity here as the equilibrium warming for a CO2 doubling, with the forcing for CO2 doubling being 5.35 W m-2).
For maximum cooling, these results show that, for any given eruption, the cooling depends approximately on the climate sensitivity raised to the power 0.37. (In LG98, from results in their Fig. 4, the corresponding power is only 0.20.) The time scale for relaxation back to the pre-eruption state is also dependent on the climate sensitivity, with slower decay for larger sensitivity (see below). A further difference from LG98 is that we find the time of peak cooling to be independent of the climate sensitivity – LG98 find that this time lags behind the time of peak forcing by 4 to 16 months, with greater lag for larger sensitivity. In our simulations, the lag varies with eruption (as a consequence of forcing differences between the hemispheres), ranging from 1 month (Novarupta) to 8 months (Agung) behind peak forcing – i.e., 3 to 13 months after the eruption for these particular volcanoes. For any given eruption, this lag is the same for all values of sensitivity.
We quantified the relaxation time scale by fitting exponential decay curves to the MAGICC results for the five largest eruptions, Santa Maria, Novarupta, Agung, El Chichon and Pinatubo. In all cases, the decay is slower than exponential for the first 12–16 months (only a few months for Novarupta), is well approximated by an exponential over the next 30–50 months, and then again slower than exponential. The slow early response is a result of the initially slow removal of aerosol from the stratosphere. The later sub-exponential decay behavior produces a long ‘tail’ in the response, although this is obscured in most cases by a subsequent eruption. It is impossible to identify this behavior in either the observations or the AOGCM results because, by the time the sub-exponential portion is reached, the residual cooling is invariably much less than 0.1oC and consequently obscured by the noise of natural variability (which has a standard deviation of about 0.17oC). For the same reason, assuming a purely exponential decay for all times provides an excellent approximation to the ‘true’ decay curve.
The best-fit exponential decay times for sensitivities of 1.0oC, 2.0oC and 4.0oC are: Santa Maria, 27, 31 and 34 months; Novarupta, 17, 19 and 21 months; Agung, 29, 34 and 39 months; El Chichon, 31, 37 and 43 months; and Pinatubo, 31, 37 and 42 months. Novarupta is anomalous here, presumably because of the high-latitude Northern Hemisphere location of this volcano compared with the much lower latitudes for the other four volcanoes (in MAGICC, this geographical influence is captured by the hemispheric differential in the applied forcing, and by the land-ocean and inter-hemispheric separations in the model). These results are entirely consistent with the decay times assumed by Santer et al. (2001). They are much longer than the decay times for forcing (approximately 12 months), a necessary consequence of the thermal inertia of the climate system.