Geophysical Research Letters
Supporting Information for
Assessing the controllability of Arctic sea ice extent by
sulfate aerosol geoengineering
L. S. Jackson1, J. A. Crook1, A. Jarvis2, D. Leedal2, A. Ridgwell3, N. Vaughan4,
and P. M. Forster1
1 Institute for Climate and Atmospheric Science, School of Earth and Environment, Maths/Earth and
Environment Building, The University of Leeds, Leeds, LS2 9JT, UK.
2 Lancaster Environment Centre, Lancaster University, LA1 4YQ, UK.
3 School of Geographical Sciences, University of Bristol, University Road, Bristol
BS8 1SS, UK.
4 Tyndall Centre for Climate Change Research, School of Environmental Sciences,
University of East
Anglia, Norwich, NR4 7TJ, UK.
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Contents of this file
1. Calibration of the Model Predictive Control (MPC) Algorithm
2. Estimation of annual radiative forcing in the MPC algorithm
3. MPC algorithm input values
4. Surrogate real world simulation of explosive volcanic eruptions during 2011-2099
5. Addition of observational noise to HadGEM2 outputs
6. Re-distribution of SO2 injections
7. Sulfate distribution
8. Description of data set “2014GL062240-ds01.txt”
Additional Supporting Information (Files uploaded separately)
MPC algorithm input data used during the simulation
2014GL062240-ds01.txt
Introduction
This file contains additional supporting information describing the data and methods used
in simulations for “Controllability of Arctic sea ice extent by sulfate aerosol
geoengineering”, manuscript #2014GL062240.
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1. Calibration of the Model Predictive Control (MPC) Algorithm
For the forecasting model exploited in the MPC we extended the MAGICC2.0 simple
climate model [Den Elzen and Lucas, 2003; Meinshausen et al., 2011] to include the
relationship between temperature and Arctic sea ice, and the impact of planned
stratospheric SO2 injections on the global energy balance. For the relationship between
northern hemisphere annual mean temperature and annual minimum Arctic sea ice area
we assumed a linear model of the form:
ySI(k) = -2.047yNH(k)
(S.1)
where k is the year, ySI the perturbation to pre-industrial steady state annual minimum
Arctic sea ice (million km2), and yNH the perturbation to pre-industrial steady state
northern hemisphere annual mean surface air temperature (°C). The regression coefficient
(-2.047 million km2 oC-1) was estimated by least-squares using data from CMIP5 [Taylor
et al., 2012] historical simulation (1850-2005), excluding HadGEM2. This parameter was
revised to -2.1 million km2 oC-1 in year 2044 after review of 2018-2043 trends in the RW
simulation for northern hemisphere annual mean temperature and annual minimum Arctic
sea ice area.
For the relationship between geoengineering injections of SO2 and the perturbation to
northern hemisphere radiative forcing, we assumed a linear dynamic model of the form:
F(k) = bIso2(k) + aF(k-1)
(S.2)
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where F is the geoengineering perturbation to annual mean northern hemisphere radiative
forcing (Wm-2), and Iso2 are the annual geoengineering SO2 injections (Tg). The
dynamics implied in equation (S.2) attempts to represent both the formation kinetics of
aerosol and, more importantly, the subsequent mixing and sedimentation dynamics in the
atmosphere. Initial estimates of the gain, b/(1-a) = -.2 W m-2 Tg-1, and time constant, ln(1/a) = 3 months, were derived from the RW response of Aerosol Optical Depth (AOD) to
the Pinatubo eruption. These estimates were revised in 2044 to -0.16 W m-2 Tg-1 and 5.6
months estimated against the AOD response to Iso2 for the period injections had been
made.
MAGICC2.0 and equations (S.1) and (S.2) are used to predict the relationship between
geoengineered SO2 emissions, Iso2, and perturbations in Artic sea ice, ySI. This is used to
predict an optimal trajectory for Iso2 in order to drive ySI from its present observed state to
its desired state over a 10 year receding horizon.
2. Estimation of annual radiative forcing in the MPC algorithm
We incorporated estimates of radiative forcing from anthropogenic greenhouse gas
(GHG) emissions, industrial SO2 emissions and explosive volcanic eruptions in the MPC
algorithm.
GHG forcing was estimated for well mixed GHGs (CO2, CH4, N2O, CFC-12, and HFC134a) using simplified analytic expressions published by the Intergovernmental Panel on
Climate Change (IPCC) [Section 6.3.5 of Ramaswamy et al., 2001]. To estimate the
aggregate GHG forcing over the MPC forecast horizon, a simple least-squares linear
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model was fitted to the 10 most recent years of GHG forcing data and then extrapolated
to estimate aggregate GHG forcing over the next 10 years.
The negative forcing attributed to incidental industrial SO2 (yIS) was estimated up to year
2039 by applying the simple linear relationship:
yIS(k) = -0.41yGHG(k) – 0.12
(S.3)
where yGHG is the estimated aggregate forcing resulting from changes in concentrations of
well mixed GHGs. The coefficients are based on values described in Shine and Forster
[1999]. Post 2039, the simple relationship of equation S.3 was replaced with constant
forcing of -0.5 Wm-2 derived following analysis of the energy balance at top of
atmosphere.
Perturbation of the annual mean northern hemisphere forcing by volcanic SO2 was
estimated by converting an estimate of the stratospheric load of SO2 (Tg) into a forcing
perturbation using equation S.2. Our estimates of the stratospheric SO2 load for the three
explosive volcanic eruptions which occurred during geoengineering were: 6 Tg SO2
(2038), 9 Tg SO2 (2044), and 6.25 Tg SO2 (2064).
3. MPC algorithm input values
Annual mean hemispheric temperatures, annual minimum ASI area, estimated
greenhouse gas and anthropogenic aerosol forcings, estimated stratospheric SO2
emissions from volcanic eruptions and SO2 injections input into the MPC algorithm are
plotted in Figure S.1 and available in the data set 2014GL062240-ds01.txt.
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4. Surrogate Real World (RW) simulation of explosive volcanic eruptions during
2011-2099
HadGEM2 simulated volcanic eruptions by applying perturbations to stratospheric
aerosol optical depth (AOD) at 0.55μm that are specified monthly for four latitudinal
regions: 45oN-90oN, 0-45oN, 0-45oS and 45oS-90oS.
Explosive volcanic eruptions during the period 2011-2099 were simulated with their
frequency and magnitude determined stochastically based on nine major eruptions during
1860-2010 [Sato et al., 1993] (Figure S.2). For each year during 2011-2099, we generated
a random number between 1850 and 2010 (inclusive and without repetition). If the
random number matched the year of eruption for one of the nine historic eruptions, a
volcanic eruption based on the matched historical eruption was simulated for that year. It
was assumed that the eruptions would perturb stratospheric AOD for up to three years
after the eruption and during this time no further eruptions were permitted.
The magnitude of each volcanic eruption was controlled through its maximum monthly
impact on stratospheric AOD. This was determined by generating a random number from
a uniform distribution between 0.05 and 0.2. For each of the four latitudinal regions, the
monthly time series of AOD perturbations was adopted from the historic eruption
sampled from the nine eruptions during 1850-2010 (Figure S.3). The monthly values
were then uniformly scaled so that the required maximum monthly AOD impact was
achieved in one month.
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5. Addition of observational noise to HadGEM2 outputs
To include the effect of observational errors, noise was added to outputs for temperature,
sea ice and top of atmosphere (TOA) energy fluxes in the ‘real world’ (RW) simulation.
The noise was assumed unbiased, normally distributed and independent from one time
period to the next. The means and standard deviations of the annual differences between
the RW ‘observed’ and the unadjusted HadGEM2 data values are listed in Table S.1 for
the period of geoengineering (2018-2074). The annual differences are shown in Figure
S.4.
6. Re-distribution of SO2 injections
SO2 injections were timed to maximise attenuation of incoming solar radiation for a
given volume of SO2. This was estimated by inverting equation (S.2) with the forcing
input, F(k), matching the weekly distribution of solar radiation for 70N. The resultant
distribution for the 2039-2074 parameterisation of equation (S.2) is shown in Figure S.5.
The fact that these emissions occur earlier in the year than the peak in solar radiation at
70N reflects the fact that it takes some time for dispersion to occur post injection.
7. Sulfate distribution
The distribution of accumulation mode sulphate aerosol is shown in Figure S.6. A
longitude x latitude map and a latitude x height profile for the last decade of
geoengineering (2065-2074) are shown for the real world (RW) and control (CTRL)
simulations.
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8. Description of data set “2014GL062240-ds01.txt”
The data set “2014GL062240-ds01.txt” lists the MPC algorithm input data used during
the simulation. Data is provided for eight fields listed in columns A-H and described in
Table S.2.
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References
Bluth, G. J. S., W. I. Rose, I. E. Sprod, and A. J. Krueger (1977), Stratospheric Loading
of Sulfur from Explosive Volcanic Eruptions, The Journal of Geology, Vol. 105, p. 671–
683.
Den Elzen, M. G. J., and P. Lucas (2003), FAIR 2.0-A decision-support tool to assess the
environmental and economic consequences of future climate regimes, www.mnp.nl/fair,
RIVM-report 550015001.
Meinshausen, M., S. C. B. Raper, and T. M. L. Wigley (2011), Emulating coupled
atmosphere-ocean and carbon cycle models with a simpler model, MAGICC6 – Part 1:
Model description and calibration, Atmos. Chem. Phys., 11, 1417-1456, doi:10.5194/acp11-1417-2011.
Ramaswamy, V., O. Boucher, J. Haigh, D. Hauglustaine, J. Haywood, G. Myhre, T.
Nakajima, G. Y. Shi, and S. Solomon (2001), Observed Climate Variability and Change.
In: Climate Change 2001: The Scientific Basis. Contribution of Working Group I to the
Third Assessment Report of the Intergovernmental Panel on Climate Change [Houghton,
J. T., Y. Ding, D. J. Griggs, M. Noguer, P. J. van der Linden, X. Dai, K. Maskell, and C.
A. Johnson (eds.)]. Cambridge University Press, Cambridge, United Kingdom and New
York, NY, USA, 881pp.
Sato, M., J. E. Hansen, M. P. McCormick, and J. B. Pollack (1993), Stratospheric aerosol
optical depths, 1850-1990. J. Geophys. Res., 98(D12), 22987–22994.
Shine, K. P., and P. M. Forster (1999), The effect of human activity on radiative forcing
of climate change: a review of recent developments, Global and Planetary Change, 20,
pp. 205-225.
Taylor, K. E., R. J. Stouffer, and G. A. Meehl (2012), An Overview of CMIP5 and the
experiment design, Bull. Amer. Meteor. Soc., 93, 485-498, doi:10.1175/BAMS-D-1100094.1.
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Table S.1 Means and standard deviations for the differences between RW ‘observed’
data values (which include observational noise) and unadjusted data values from
HadGEM2 for the period of geoengineering (2018-2074).
Annual mean northern hemisphere temperature (oC)
Difference between
‘observed’ and unadjusted values
Mean
Standard deviation
0.004
0.023
Annual mean southern hemisphere temperature (oC)
-0.002
0.045
Annual minimum Arctic sea ice area (million km2)
0.095
0.160
Annual mean TOA net radiation flux (Wm-2)
0.001
0.031
Table S.2 Description of data set file 2014GL062240-ds01.txt
Field
Description
A
Year
B
Northern hemisphere annual mean temperature (oC)
C
Southern hemisphere annual mean temperature (oC)
D
Annual minimum Arctic sea ice area (km sq)
E
Annual SO2 injection mass (Tg)
F
Estimated anthropogenic greenhouse gas forcing (Wm-2)
G
Estimated aerosol forcing from industrial emissions (Wm-2)
H
Estimated stratospheric SO2 emissions from volcanic eruptions (Tg)
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