A. Robock: Comment on ‘‘Climate forcing by the volcanic eruption of Mount Pinatubo’’ by David H. Douglass and Robert S. Knox

Readers who want the equations and variables in the correct format had better go straight to the link to the pdf file of this article:

http://climate.envsci.rutgers.edu/pdf/DouglassKnoxComment2005GL023287.pdf

Comment on ‘‘Climate forcing by the volcanic eruption of Mount Pinatubo’’ by David H. Douglass and Robert S. Knox

Alan Robock (Department of Environmental Sciences, Rutgers University, New Brunswick, NJ, U.S.A.)

Received 20 April 2005; accepted 27 July 2005; published 25 October 2005.

Citation: Robock, A. (2005), Comment on ‘‘Climate forcing by the volcanic eruption of Mount Pinatubo’’ by David H. Douglass and Robert S. Knox, Geophys. Res. Lett., 32, L20711,
doi:10.1029/2005GL023287.

[1] Douglass and Knox [2005, hereinafter referred to as DK] present a confusing and erroneous description of limate feedbacks and the climate response to the 1991 Mt. Pinatubo eruption. Their conclusions of a negative climate feedback and small climate sensitivity to volcanic forcing are not supported by their arguments or the observational evidence. As pointed out by Wigley et al. [2005a], this is the consequence of assuming a one-box representation for the climate system, and ignoring energy exchange with the deep ocean.

[2] In the description of their analysis, DK make a fundamental mistake in describing the problem. They claim to use ‘‘standard linear response theory,’’ but they confuse the response with the forcing. They say, ‘‘The LW [longwave] effect is by definition the forcing function DF for the climate, represented by the measured surface temperature anomaly DT.’’ LW radiation changes, however, are produced by both the presence of a forcing agent, in this case stratospheric aerosols, and the response of the climate system. It is the instantaneous net radiation change with no response that is the forcing. The temperature anomaly is the response to forcing, and not the forcing itself, and the LW changes reflect both the true forcing and the effects of the temperature response.

[3] In spite of their statement to the contrary, DK apparently do use the correct forcing, as characterized by their equation (5) and illustrated in their Figure 2. Confusion arises because the forcing they use is a scaled version of the estimated aerosol optical depth changes, which represents the true forcing, yet they continually refer to the scaled optical depth as the LW changes. That the two items are different is clear from DK’s Figure 1.

[4] The forcing of climate change can be defined as the change in the net radiation at the top of the atmosphere, the tropopause, or the surface, without any response of the climate system, or allowing for the stratosphere to equilibrate. Stenchikov and Robock [1995], Houghton et al. [1996], and Hansen et al. [2005] discuss the standard definitions of radiative forcing and considerations for forcing from aerosols, which are not uniformly mixed in the atmosphere. For our purposes, it is sufficient to consider the forcing at the top of the atmosphere, allowing for no equilibration [Stenchikov & Robock, 1995; Stenchikov et al., 1998]. This forcing can be defined as:

(see link for the equations)

where DQ(t) is the radiative forcing, DSW(t) is the change in net downward shortwave radiation and DLW(t) is the change in net downward longwave radiation. Minnis et al. [1993] provide observations of changes in SW and LW separately after the 1991 Mt. Pinatubo eruption, but, of course, these observations combine the effects of forcing and response. Nevertheless, the SW changes are the largest, by an order of magnitude, and dominate the forcing. One cannot do a correct analysis if SW changes are ignored.

[5] Consider a global-average, time-dependent, anomaly energy-balance climate model:

(see link for equation)

where C is the heat capacity, DT(t) is the change in global temperature, l is the climate sensitivity (l = dT dQ), and DQ(t) is the externally applied radiative perturbation. (Much of the climate literature uses l1 or S as the climate sensitivity, but here the same nomenclature as DK is used to avoid confusion.) For a step-function forcing, at steady state the first term in (2) goes to zero and the final temperature change is:

(see link to pdf file for equation)

If DQ is due to a doubling of CO2, then DT is called DT2x. It is now conventional to characterize l in units of DT2x. The e-folding time scale of climate response is t (t = Cl). The amplitude of the climate response and the time it takes to respond to an episodic forcing are both dependent on DT2x.

[6] The value of l proposed by DK, 0.15 K/(W m2), corresponds to an unrealistic value of DT2x of 0.6 K. There is no evidence in the record of past climate change or in climate model simulations that the climate sensitivity could be so low.

[7] Soden et al. [2002] conducted general circulation model (GCM) simulations with the Geophysical Fluid Dynamics Laboratory Manabe climate model, forced by the observed distribution of Pinatubo aerosols. When run with prescribed clouds, their climate model, which has a DT2x  3.0 K, accurately reproduced not only the observed surface air temperature, but also the observed upper tropospheric humidity changes (consistent with a positive water vapor feedback), and the observed top of atmospherechanges in both SW and LW. To investigate feedbacks further, Soden et al. used two different versions of the model with explicitly modified sensitivity: the standard configuration, and a configuration with no water vapor feedback. Both GCMs had the same mixed-layer ocean heat capacity and were driven with the same forcing. The integrated cooling in the ‘‘no water vapor feedback’’ configuration was only 60% of that from the model with water vapor feedback. This is consistent with what one would expect for a gain factor of 0.4 from water vapor feedback (which is the expected value under the assumption of constant relative humidity), i.e., lðwith water vaporÞ ¼ lðno water vaporÞ ð1  0:4Þ: ð4Þ

Because they were able to observe each component of the feedback process, including the reduction of upper tropospheric water vapor with the Pinatubo-induced global cooling (a positive water vapor feedback), the Soden et al. study correctly showed how the Pinatubo eruption can be used to diagnose the sensitivity of the climate system and demonstrated that the sensitivity was in the conventional range.

[8] Wigley et al. [2005b], using a very different approach, obtained the same result as Soden et al. [2002]. They clearly showed that for episodic forcing, the transient temperature response of the climate system depends on C and DT2x, as characterized by both the maximum temperature change (DTmax) and the time scale of the response. (The response time in the Wigley et al. study is that for relaxation back to an equilibrium state, a time scale specific to volcanic forcing. It is called tV here, with the V used to indicate that it is specific to the volcanic forcing case. This time scale is not the same as the time scale that DK attempt to calculate, although they appear to think that it is.) Wigley et al. assigned to their MAGICC energy balance, upwelling diffusion climate model the same sensitivity as the National Center for Atmospheric Research PCM coupled ocean-atmosphere GCM. They found that, with this sensitivity, the MAGICC volcano results accurately matched the GCM, giving both the correct time scale and amplitude of climate response to volcanic eruptions, confirming that MAGICC can be used to measure the sensitivity of the climate system.

[9] Wigley et al. [2005b] then compared the results of MAGICC simulations with different sensitivities to the observed climate response after different eruptions. They found that DTmax / (DT2x)0.20 and tV [months] = 30 (DT2x)0.23. This is in contrast to the results of Lindzen and Giannitsis [1998], whose climate model results are inconsistent with GCM results. Lindzen and Giannitsis had found that DTmax / (DT2x)0.37 and tV = 57 (DT2x)0.41 and they erroneously implied from this that DT2x was quite low. By analyzing the observed temperature changes in response to the 1963 Agung eruption and the 1991 Pinatubo eruption, and fitting the response to their MAGICC model, Wigley et al. found that DT2x = 2.8 K for the 1963 Agung eruption and DT2x = 3.0 K for Pinatubo, and that tV = 38 months for both cases.

[10] As shown by the above two climate model analyses, in which the time delay and inertia of the ocean areexplicitly accounted for in the model physics, we expect the climate system to have a DT2x of about 3.0 K and for the peak cooling response after Pinatubo to be about 30% of the equilibrium response. The sensitivity calculated by DK, l = 0.15 K/(W m2), corresponding to DT2x of 0.6 K, means that if we use the observed maximum forcing of about 3.0 W m2 [0.165 (DK, Figure 2) times A (18.5 W m2/K, the mean of the DK values, 16 to 21Wm2/K)], the actual DTmax of 0.45 K (DK, Figure 3) is exactly equal to the equilibrium climate response we can expect (l x forcing) if the forcing were maintained. This is clearly wrong. Their failure to properly account for the entire climate system has led them to derive a climate sensitivity and response time that are much too small.

[11] To summarize, if the analysis is done correctly, the 1991 Mt. Pinatubo eruption serves as a valid test of the response of the climate system to external forcing [Robock, 2003]. As also discussed by Kerr [2004], this test provides additional evidence that the sensitivity of the climate system to doubling CO2 (DT2x) is about 3 K and that the water vapor greenhouse feedback is positive and can be observed.