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Auxiliary material for
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Analyses of New Short-Lived Replacements for HFCs with Large GWPs
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Donald J. Wuebbles,1 Dong Wang,1,2 Kenneth O. Patten1 and Seth C. Olsen1
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1
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Illinois 61801, USA.
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2
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Italy.
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Department of Atmospheric Sciences, University of Illinois, 105 South Gregory Street, Urbana,
Now at: Euro-Mediterranean Centre for Climate Change, viale Aldo Moro, 44, Bologna 40127,
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Supplementary Materials
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1. Simple lifetime estimation approaches used in previous studies
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Assuming globally-averaged OH concentration
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X 
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where NOH is global weighted-average OH concentration.
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Scaling from CH3CCl3 lifetime
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X C HC C l C HC COl H
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2. Simple GWP estimation approach using HGWP
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In the previous studies (Hurley et al., 2007, Nielsen et al., 2007; Sondergaard et al., 2007;
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Sulbaek Andersen et al., 2008) the GWPs for these VSLS are estimated through the Halocarbon
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Global Warming Potential (HGWP) as described in Fisher et al. (1990), over time horizon t H
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defined as the ratio of the GWP for gas X to that for CFC-11
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GW P
(t H )
X (t H )  HGW P
X (t H )  GW P
C F 
C1 1
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HGWPX(tH) for gas X is obtained by
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HGWPX (t H )  (
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Where MX, MCFC-11, τX, τCFC-11, IFX, and IFCFC-11 are the molecular weights, atmospheric
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lifetimes, and instantaneous forcings for gas X and CFC-11, respectively. Note in the estimation
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(M1)
k X OH NOH
k
3
3
3
3
kXO H
 M
IF X
1  exp(t H /  X )
)( X CFC 11 )(
)
IFCFC 11  CFC 11 M X 1  exp(t H /  CFC 11 )
(M2)
(M3)
(M4)
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approach the instantaneous forcings for the VSLS are calculated following Pinnock et al. (1995)
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assuming constant mixing ratios in the atmosphere.
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3. Lifetime calculation from 3-D model output
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The atmospheric lifetime (τX) of a gas X is determined as the ratio of its burden X in the
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atmosphere over the total sink of X. Lifetime can be calculated by integrating its burden and sink
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throughout the whole atmosphere, as shown in Eq. M5
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X 
 [ X ]
V ,t
 k
X OH
NV ,t dVdt
(M5)
[ X ]V ,t [OH ]V ,t NV2 ,t dVdt
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Where kX+OH is the rate constant of the reaction of X and OH, [X]V,t, [OH]V,t, and NV,t the mixing
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ratios of X and OH and number of air molecules per unit volume, respectively, in the volume
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element of interest (V) at time t.
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Eq. M1 is a simplified form of Eq. M5 if kX+OH is not dependent on temperature, [X] is nearly
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constant throughout the atmosphere, and
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NO H 
 [OH ]
 N
V ,t
N v2,t d V d t
V ,t
d Vd t
(M6)
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However, [X] is highly variable in the atmosphere for very short-lived substances. Therefore,
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neither Eq. M1 nor Eq. M2 is adequate to calculate atmospheric lifetimes for very short-lived.
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4. AGWP and radiative forcing caused by sustained emission
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It is well established that atmospheric concentration of a gas, whose sink is dependent on its
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concentration to the first order, will decay exponentially after emission into the atmosphere.
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Accordingly, for a gas X whose efficiency in changing radiative forcing is proportional to its
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mass (for a given atmospheric distribution) in the atmosphere, the radiative forcing caused by a
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pulse emission of one unit mass X, decays exponentially following
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t
RFp (t)  Fo e x p( )
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where F0 is the instantaneous radiative forcing at the time t is injected into the atmosphere, and
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τX atmospheric lifetime of gas X. Hence AGWP, or time-integrated radiative forcing, over time
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horizon tH for gas X can be derived as the following
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AGW P   RFp (t ) d t   F0 ex p (
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The conventionally chosen time horizons for GWP comparisons are 20-, 100-, and 500-years
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(IPCC, 1990). The atmospheric lifetimes of the VSLS considered here are all less than 1 month,
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i.e. tH   x . Hence, for these VSLS
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AGWP  F0 x
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On the other hand, the UIUC RTM calculates the radiative forcing change due to sustained
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emission of a gas. The following deduction shows that the AGWP of X just equals the radiative
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forcing caused by sustained X emissions.
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Considering a sustained emission such that one unit mass X is emitted in one unit time, the
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radiative forcing caused by such sustained emission at time t can be calculated
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RF s (t)   RF p (u  t)du   F0 exp( 
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If t is sufficiently longer than τx,
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RFs  F0x
(M7)
x
tH
tH
0
0
t
x
)d t F0 x [1  ex p (
tH
x
)]
(M8)
(M9)
t
t
t u
0
0
x
)du  F0 x[1 exp( 
t
x
)]
(M10)
(M11)
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The above derivation (Eqns. M9 and M11) shows that for a VSLS, both the AGWP and radiative
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forcing caused by sustained emission of the strength one unit mass per unit time is equal to the
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product of F0 and its atmospheric lifetime. For a more general derivation see Prather [2002].
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References for Supplementary Materials
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Fisher, D. A., C. H. Hales, W. C. Wang, M. K. W. Ko, and N. D. Sze (1990) Model-calculations
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of the relative effects of CFCs and their replacements on global warming. Nature, 344, 513-516.
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Hurley, M. D., J. C. Ball, and T. J. Wallington (2007) Atmospheric chemistry of the Z and E
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isomers of CF3CF=CHF; Kinetics, mechanisms, and products of gas-phase reactions with Cl
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atoms, OH radicals, and O3, J. Phys Chem A, 111, 9789-9795 (2007).
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Nielsen, O. J., M.S. Javadi, M. P. Sulbaek Andersen, M. D. Hurley, T. J. Wallington, and R.
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Singh (2007) Atmospheric chemistry of CF3CF=CH2: Kinetics and mechanisms of gas-phase
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reactions with Cl atoms, OH radicals, and O3, Chem. Phys. Lett., 439, 18-22.
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Pinnock, S., M. D. Hurley, K. P. Shine, T. J. Wallington, and T. J. Smyth (1995) Radiative
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forcing of climate by hydrochlorofluorocarbons and hydrofluorocarbons, J. Geophys. Res.-
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Atmospheres, 100, 23227-23238.
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Sondergaard, R., Nielsen, O. J., Hurley, M. D., Wallington, T. J. and R. Singh (2007)
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Atmospheric chemistry of trans-CF3CH = CHF: Kinetics of the gas-phase reactions with Cl
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atoms, OH radicals, and O3, Chemical Physics Letters, 443, 199-204.
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Sulbaek Andersen, M. P., E. J. K. Nillson, O. J. Nielsen, M. S. Johnson, M.D. Hurley and T. J.
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Wallington (2008) Atmospheric chemistry of trans-CF3CH = CHCl: Kinetics of the gas-phase
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reactions with Cl atoms, OH radicals, and O3, J. Photochem. Photobiol., A-Chemistry, 199, 92-
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97.
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