2. SUMMARY AND GOALS • To identify the volcanic response signal in the signal+noise of a set of AOGCM runs (PCM) • To see how well this signal can be reproduced with a simple upwelling-diffusion energy-balance climate model • To use the UD EBM to determine the characteristics of volcanic response and how these vary with the climate sensitivity

3. PCM experiments with volcanic forcing • Volcanoes only • Solar + Volcanoes • Solar, Volcanoes and Ozone • ‘ALL’ = S, V, O + Greenhouse gases + direct sulfate Aerosols

4. IDENTIFYING THE VOLCANO SIGNAL WITH PCM

5. Variability summary (monthly data over 1890–1999)
Number
Experiment
Mean S.D.
(degC)
S.D. of Ensem. Ave. 1
Control
0.171
0.085 2 V
0.191
0.121 3 SV
0.195
0.131 4
OSV
0.199
0.134 5
ALL
0.271
0.232 6
Observed
0.248

6. Variability of ensem-ave volcano cases (monthly data over 1890 –1999)
Number
Combination
S.D. (degC) 1 V
0.121 2
SV-V
0.139 3
OSV-OS
0.144 4
ALL-GAOS
0.154 5
( )/4.0
0.101
Control
0.0851
V – Vsignal
0.0905
5 – Vsignal
0.0604

7. Ensemble averaging: n=1 to 4
Eruption dates for Santa Maria, Agung, El Chichon and Pinatubo marked.
Note how difficult it is to estimate the maximum cooling signals with only one realization.

8. Ensemble averaging: n=4 to 16
Eruption dates for Santa Maria, Agung, El Chichon and Pinatubo marked

9. IDENTIFYING THE VOLCANO SIGNAL WITH AN UPWELLING-DIFFUSION ENERGY-BALANCE MODEL (MAGICC)

10. IDENTIFYING THE SIGNAL WITH MAGICC: METHOD • Use MAGICC model parameters from IPCC Ch. 9 based on fit to 1% compound CO2 CMIP simulation (note that this is decadal timescale forcing, while the volcanic forcing is on a monthly timescale) • Drive MAGICC with forcing used in the PCM experiments (from Caspar Ammann)

11. VOLCANIC ERUPTION SIGNAL 16-member ensemble-mean from PCM [signal plus noise] compared with simulation using the simple UD EBM ‘MAGICC’ [pure signal].

12. The excellent fit between the MAGICC and PCM results, the fact that MAGICC gives a ‘pure’ signal, and the fact that the climate sensitivity is a user-input parameter in MAGICC means that we can use MAGICC to obtain greater insight into the character of the volcanic forcing response signal.

13. Simple energy balance equation
C dDT/dt + DT/S = Q(t) = A sin(wt).
The solution is
DT(t) = [(wt)2/(1+(wt)2)] exp(-t/t) + [S/(1+(wt)2)][A{sin(wt) – wt cos(wt)}]
where t is a characteristic time scale for the system, t = SC.
Low-frequency forcing (w << 1/t), solution is simply the equilibrium response
DT(t) = S A sin(wt)
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.
High-frequency case (w >> 1/t) the solution is
DT(t) = [A/(wC)] sin(wt – p/2)
showing a quarter cycle lag of response behind forcing, with the response being independent of the climate sensitivity.

14. EFFECT OF CLIMATE SENSITIVITY ON THE RESPONSE TO VOLCANIC FORCING

15. SIMULATED PINATUBO ERUPTION

16. PEAK COOLING AS A FUNCTION OF CLIMATE SENSITIVITY
DT2x
(degC)
Santa Maria
Agung
El Chichon
Pinatubo
1.0
0.258
[1.00]
0.265
0.259
0.394
2.0
0.348
[1.35]
0.357
0.349
0.533
4.0
0.430
[1.67]
0.439
[1.66]
0.429
0.658
Peak cooling is closely proportional to peak forcing (3%)

17. DECAY TIME AS A FUNCTION OF CLIMATE SENSITIVITY
DT2x
(degC)
Santa Maria
Agung
El Chichon
Pinatubo
1.0 26
[months] 28 30
2.0 33 36
4.0 34 38 42 41
Relaxation back to the initial state is slightly slower than exponential, so the apparent e-folding time increases with time. The above are minimum e-folding times.

18. CONCLUSIONS • Peak cooling is relatively insensitive to DT2x [DTmax(DT2x)  DTmax(1) + a ln(DT2x)] • Relaxation time is 26–42 months, logarithmic in DT2x • Observed peak coolings can be used to estimate DT2x, but uncertainties are large due to internal variability noise in the observations • Long timescale response cannot be used to estimate DT2x because the residual signal is too small relative to internal variability noise [contrast with Lindzen and Giannitsis, 1998)]