Supplement to “ Air-snowpack exchange of bromine , ozone and mercury in the springtime Arctic simulated by the 1-D model PHANTAS – Part 2 : Mercury and its speciation ”

Donohoue et al. (2006) conducted a laboratory kinetic study to determine the rate coefficient for the reaction (RS1) using N2 as a buffer gas for the temperature range of 243–293 K and the pressure range of 200–600 Torr (760 Torr = 1 atm) and using He as a buffer gas for the pressure range of 200– 600 Torr at room temperature. They fitted the experimental results in the N2 buffer gas to a temperature-dependent, thirdorder rate coefficient (in cm molecule−2 s−1):

An initial step for the oxidation of Hg(0) in the gas phase is a Br-attack on Hg(0): Hg + Br (+M) → HgBr (+M). (RS1) Subsequently, part of HgBr undergoes a thermal decomposition back to Hg(0) and Br: which is competed by further reactions of HgBr to form thermally stable products such as HgBr 2 : HgBr + Br (+M) → HgBr 2 (+M).

(RS3)
According to a quantum mechanics study by Balabanov et al. (2005), there are two other product channels for the reaction HgBr + Br, viz.Br-exchange (RS4) and Br-abstraction (RS5): HgBr + Br → BrHg + Br (RS4) → Hg + Br 2 . (RS5) Below, we summarize what is known about rate constant for each of these reactions, on the basis of our literature survey.
S1.1 Hg + Br + M → HgBr + M (RS1) Donohoue et al. (2006) conducted a laboratory kinetic study to determine the rate coefficient for the reaction (RS1) using N 2 as a buffer gas for the temperature range of 243-293 K and the pressure range of 200-600 Torr (760 Torr = 1 atm) and using He as a buffer gas for the pressure range of 200-600 Torr at room temperature.They fitted the experimental results in the N 2 buffer gas to a temperature-dependent, thirdorder rate coefficient (in cm 6 molecule −2 s −1 ): (1.46 ± 0.34) × 10 −32 × T 298 −1.86±1.49 .
On the theoretical side, by using the Rice-Ramsberg-Kassel-Marcus (RRKM) theory with ab initio calculations of bond energies at the B3LYP level of theory, Goodsite et al. (2012) derived the third-order rate constant (in cm 6 molecule −2 s −1 ) for the same reaction at T = 200-300 K: which gives values in excellent agreement with experimentally derived ones by Donohoue et al. (2006).Shepler et al. (2007) used a higher level of theory, viz.CCSD(T) (coupled cluster theory with single and double excitations and a perturbative treatment of triple excitations) for ab initio calculations to construct the potential energy surface of the reaction dynamics for Hg + Br + Ar → HgBr + Ar, which is then used to derive the temperature-dependent rate constant (in cm 6 molecule −2 s −1 ) by the quasi-classical trajectories (QCT) method: .
Between 200-320 K, this rate constant by Shepler et al. (2007) gives values 2-to 3-fold greater than those derived by Donohoue et al. (2006) and Goodsite et al. (2012).Even higher rate constants were derived by earlier theoretical calculations in Khalizov et al. (2003) employing a transition state theory and in Goodsite et al. (2004) (although revised later to lower rate values by the same authors; see above) employing the RRKM theory (Fig. S1; see also Shepler et al. (2007)).

S1.2 HgBr + M → Hg + Br + M (RS2)
There has been no experimental determination but theoretical calculations of the rate constant for this reaction.By using the same methodology to derive the rate constant for RS1 (see Sect.S1.1), Goodsite et al. (2012) obtained the following first-order expression (in the unit of s −1 ) for RS2 with M = N 2 at 1 atm and between 200-300 K: If we assume a low-pressure limit behavior for RS2, we may re-write this rate constant in the second-order expression (in cm 3 molecule −1 s −1 ): On the order hand, by using the CCSD(T)-derived potential energy surface with the QCT-based rate coefficient calculations, Shepler et al. (2007) derived the following secondorder rate constant (in cm 3 molecule −1 s −1 ) for RS2 with M = Ar: which gives values 4-to 5-fold greater than those derived by Goodsite et al. (2012) between T = 200-320 K (see Fig. S2).Although the rate coefficient was not calculated directly, Dibble et al. (2012Dibble et al. ( , 2013) ) calculated the bond energy of HgBr by the CCSD(T) level of theory and derived a thermodynamic equilibrium constant (in cm 3 molecule −1 ) for the reactions RS1 and RS2, viz.Hg + Br + M = HgBr + M, as K eq = (9.14 ± 0.06) × 10 −24 exp 7801 ± 201 T .
By combining this equilibrium constant with the rate constant for RS1 taken from Donohoue et al. (2006) Again, there is no experimental determination of rate constants for RS3, RS4 and RS5.By using the RRKM theory with ab initio calculations of bond energies at the B3LYP level of theory, Goodsite et al. (2004) derived the rate constant (in cm 3 molecule −1 s −1 ) for RS3 with M = N 2 at 1 atm and between 180-400 K: where the reaction was noted to be close to the high-pressure limit at 1 atm and thus the second-order expression was rationalized.Goodsite et al. (2012), however, later revised input parameters for the molecular properties of HgBr and then re-calculated the rate constants for RS1 and RS2.Unfortunately, the rate constant for RS3 was not re-calculated in Comparison between rate constants for the reaction (RS2) in the first-order expression at 1 atm calculated theoretically (Goodsite et al., 2004(Goodsite et al., , 2012;;Shepler et al., 2007).

Goodsite et al. (2012)
. Balabanov et al. (2005) employed the CCSD(T) level of theory with the QCT method, viz. the same methodology as employed by Shepler et al. (2007) for the rate constant calculations for RS1 and RS2, to derive the rate constants (in cm 3 molecule −1 s −1 ) for RS3, RS4 and RS5 at 298 K: The k RS3, Balabanov−QCT value calculated by Balabanov et al. (2005) is a factor of eight lower than the k RS3, Goodsite value calculated by Goodsite et al. (2004) at 298 K. Balabanov et al. attributed this discrepancy primarily to the lower level of theory (i.e., the B3LYP method) employed by Goodsite et al. to estimate input parameters for the RRKM calculation.Also noted by Balabanov et al. (2005) was that their QCT-derived rate constants for RS3-RS5 represented the reactions in the low-pressure limit and hence may have underestimated the collision-induced deactivation of the exited states of HgBr 2 along the trajectories of reaction dynamics.They speculated that, by taking this effect into account, the branching ratio between the Br-addition channel (RS3) and the Br-exchange channel (RS4) could be adjusted towards a higher value of k RS3, Balabanov−QCT and a lower value of k RS4, Balabanov−QCT .It should be noted, however, that the sum of k RS3, Balabanov−QCT and k RS4, Balabanov−QCT is still a factor of 3.6 lower than k RS3, Goodsite at 298 K.

S1.4 HgBr + X → HgBrX
In addition to the bond energy of BrHg-Br, Goodsite et al. (2004) calculated the bond energies of BrHg-I and BrHg-OH and found them to be only slightly lower than that of BrHg-Br, indicating the involvement of I-atoms and OH-radicals in the formation of divalent mercury in the background tropospheric air.On the basis of bond energies calculated by the CCSD(T) level of theory, Dibble et al. (2012) indicated that the reactions of HgBr with HO 2 , NO 2 , BrO and ClO would also be viable in the atmosphere.
S2 GEM, GOM and PBM simulated with a scenario of "fast" in-snow Hg(II) photo-reduction To supplement our discussion in Sect.3.2 of the main paper, we present time-height/depth cross sections for gaseous elemental mercury (GEM), gaseous oxidized mercury (GOM) and particulate-bound mercury (PBM) in the entire model domains simulated at U 2 = 2.0 m s −1 , 4.5 m s −1 and 8.5 m s −1 with scenario 1B, i.e., "fast" in-snow Hg(II) photoreduction scenario (Fig. S3a-c, for comparison with Fig. 3ac in the main paper).Also shown are the time series for the simulated mixing ratios of GEM in the ambient air and in the snowpack interstitial air (SIA) from model runs using scenarios 1A (i.e., "slow" in-snow Hg(II) photo-reduction scenario) and 1B (Fig. S4a-c).
Fig. S4.Time series for the simulated mixing ratios of GEM in the ambient air at the height of 1.5 m (solid lines) and in the SIA at the depth of 3.5 cm (dotted lines) from model runs employing scenarios 1A ("slow" in-snow Hg(II) photo-reduction scenario, red lines) and 1B ("fast" in-snow Hg(II) photo-reduction scenario, green lines) at U2 = 2.0 m s −1 (a), 4.5 m s −1 (b), and 8.5 m s −1 (c).
S3 Sensitivity of the apparent dry deposition velocities of GOM species to temperature and LLL volume Fig. S5a-i shows apparent dry deposition velocities (v * d ) of GOM and its each component species calculated at the height of 1.5 m in the air from a sensitivity study where temperature is raised from 253 K to 268 K and 298 K just for calculating the thermodynamic constants related to the partitioning of mercury between gas-and aqueous-phases discussed in Sect.3.3 (see also Fig. 6a-b) of the main paper.With increasing temperatures, Henry's law for the Hg(II) gases and the stability of their coordinated complexes with halide anions are predicted to increase generally.However, the impact of changing temperature from 253 K to 268 K is not significant for the "dry deposition" of GOM on the snow surface in our simulated conditions.On the other hand, the v * d values for GOM are more than halved by raising the temperature from 253 K to 298 K.In all cases, the value of v * d for GOM drops notably after day 4, by the saturation of Hg(II) that has been deposited in the top layer of the snowpack.
Owing to the limited capacity of PHANTAS in simulating the precipitation of salts from freezing brine, we have decided that problems associated with temperature dependence in the physical and chemical processes are not addressed in this study except for a few sensitivity runs and that model runs are conducted generally at the temperature of 253 K (see Sect. 2.3 in the main paper).To investigate how sensitive the behavior of GOM is to the volume of liquid-like layer (LLL) in the snowpack in terms of deposition from the atmosphere to the snow surface, we have conducted three sensitivity runs (at U 2 = 4.5 m s −1 ).The first sensitivity run assumes 268 K, instead of 253 K, for temperature in the whole model domain; in this case, our thermodynamic equation based on Cho et al. (2002) predicts an approximately 5 times greater volume for the LLL in the snowpack.The second and third sensitivity runs assume the temperature of 253 K in the whole model domain, but the snowpack LLL volume is increased and decreased, respectively, 5-fold from the prediction by the Cho et al. equation.It should be noted that these changes not only influence physical parameters that control the partitioning behavior of GOM between the SIA and the LLL but also modify the behavior of halogens that affect the rate of mercury oxidation in the gas phase (i.e., GOM production) and the concentrations of halide anions available for the formation of coordinated Hg(II) ligands in the LLL.
The v * d values of the GOM species as simulated in these sensitivity runs are shown in Fig. S6a-i.Although we see some notable difference in how v * d changes with time for each species of GOM, the values of v * d for the sum of GOM do not change very much between the model runs.Hence, within the limitation of our LLL approach for the representation of multiphase chemistry involving the surface of snow gains, the dry deposition of GOM is limited largely by aerodynamic resistance on the Arctic coastal and marine snow surfaces at temperatures below 268 K.

S4 Additional figures on the time series of GEM, GOM and PBM in ambient air
To supplement our discussion in Sect.3.4 of the main paper, time series for the simulated mixing ratios of GEM at 1.5 m in the ambient air and their daily trends between 5-19 h local solar time are shown from model runs using scenarios 1A, 1C, 2A, 2C, 3A, 3C, 4A and 4C (Fig. S7a-c).Also shown are the time series for the simulated mixing ratios of GEM, GOM and PBM from model runs using scenarios 2A and 2C (Fig. S8a-c), scenarios 3A and 3C S9a-c), and scenarios 4A and 4C (Fig. S10a-c), for comparison with model runs using scenarios 1A and 1C (Fig. 7a-c in the main paper).

S5 Additional figures on the relationship between BrO columns and the deposition of mercury from the air
In Sect.3.5 of the main paper (Fig. 11a-f), we showed simulated correlations between the atmospheric column amount of BrO and the net deposition of mercury from the atmosphere for model runs using scenarios 1A-C.Here we show   2 of the main paper, (b) and (e) scenario 2B using the same chemical mechanism as scenario 2A except using faster photo-reduction rates for dissolved Hg(II) in the snowpack, and (c) and (f) scenario 2C using the same rate constants as scenario 2A except with the gas-phase reaction HgBr + BrO being switched off.
the same correlation plots for model runs using scenarios 2A-C, 3A-C and 4A-C in Figs.S11a-f, S12a-f and S13a-f, respectively.

Fig. S5 .
Fig.S5.Apparent dry deposition velocities of GOM and its each component species (except Hg(OH)2, which constitutes a minimal partitioning in GOM simulated here) at 1.5 m above the snow surface from a model run using scenario 1A of mercury chemistry at U2 = 4.5 m s −1 and T = 253 K (red lines) and from two sensitivity runs where T = 268 K (blue lines) and 298 K (green lines) are assumed for the calculations of Henry's law (KH) and aqueous-phase stability constants (Keq) of Hg(II) species: (a) the sum of all GOM species, (b) HgCl2, (c) HgBr, (d) HgBr2, (e) Hg(OH)Cl, (f) Hg(OH)Br, (g) Hg(O)Br, (h) Hg(OBr)Br, and (i) HgClBr.Note that red lines in this figure denote results from the same run shown by green lines in Fig.5a-i of the main paper.
Fig.S6.The same as Fig.S5a-i but from a model run using scenario 1A of mercury chemistry at T = 253 K (red lines) as a reference, and from three sensitivity runs at T = 268 K (green lines), T = 253 K with the snowpack LLL volume increased 5-fold from our thermodynamic model prediction (blue lines), and T = 253 K with the snowpack LLL volume decreased 5-fold from our thermodynamic model prediction (violet lines).U2 = 4.5 m s −1 for all the model runs.

Fig. S7 .
Fig.S7.Temporal evolution for the mixing ratios of GEM and their daily trends between 5-19 h local solar time at the height of 1.5 m in the ambient air from model runs employing scenarios 1-4A and 1-4C at U2 = 2.0 m s −1 (a), 4.5 m s −1 (b), and 8.5 m s −1 (c).Solid and dotted lines (or solid and hatched bars for the trends) represent model runs with the gas-phase reaction HgBr + BrO switched on (scenarios 1A, 2A, 3A and 4A) and off (scenarios 1C, 2C, 3C and 4C), respectively.
Fig.S11.Correlations between the daytime column amount of BrO in the atmosphere and the daily net deposition of mercury, either excluding GEM (a-c) or including GEM (d-f), from the atmosphere to the snowpack on each simulated day (Day 1 to 8) in model runs at U2 = 2.0 m s −1 , 4.5 m s −1 , 8.5 m s −1 , and 12.0 m s −1 : (a) and (d) scenario 2A using a default chemical mechanism and adapted rate constants as listed in Table2of the main paper, (b) and (e) scenario 2B using the same chemical mechanism as scenario 2A except using faster photo-reduction rates for dissolved Hg(II) in the snowpack, and (c) and (f) scenario 2C using the same rate constants as scenario 2A except with the gas-phase reaction HgBr + BrO being switched off.
Fig. S12.The same as Fig. S11 but showing results from scenarios 3A-C.