4.12 Sulfur Chemistry

It is also possible to set CAM to predict sulfate aerosols. These aerosols can be run as passive (non-interacting) constituents, or the model can be set to allow sulfate to interact with the radiative transfer formulation. The CAM 3.0 release of the model allows only the direct radiative effect of the aerosols, although it is a straightforward modification of the model to allow indirect effects as well.

The formulation for the parameterization follows closely that described in Barth et al. [12] and Rasch et al. [143]. The module was used to examine the influence of sulfate aerosols on the atmospheric radiation budget in [92] The standard emission inventory used for prognostic aerosols is not the same as that used to produce the climatological prescribed sulfate aerosols described in section 4.8.3.

The sulfur chemistry represented in the model includes emissions, transport, gas and aqueous reactions, and wet and dry deposition of DMS, SO$_2$, SO$_4^{2-}$, and H$_2$O$_2$. Sources and sinks represented in the description of the sulfur cycle include emissions of DMS and anthropogenic sulfur, gas-phase oxidation of DMS and SO$_2$, gas-phase production and destruction of H$_2$O$_2$, aqueous-phase oxidation of S(IV) by H$_2$O$_2$ and O$_3$, dry deposition of H$_2$O$_2$, SO$_2$, and aerosol sulfate, and wet deposition of H$_2$O$_2$, SO$_2$, and aerosol sulfate.

Transport processes of trace gases and aerosols include resolved-scale advection and subgrid-scale convection and diffusion. The convective transport of trace gases and aerosols is performed on the interstitial fraction of these species in the cloudy volume and the fraction of dissolved material in the cloud drops that do not undergo microphysical transformation to precipitation. The species can be can be detrained at higher levels in the model by the convective processes.

4.12.1 Emissions

Emissions of sulfur species in the model include anthropogenic emissions of SO$_2$ and SO$_4^{2-}$ and oceanic emissions of DMS; volcanic and biomass burning sources currently are excluded. Anthropogenic emissions come from the [162] inventory. The seasonally averaged emissions data were provided at the surface and at 100 m and above to accommodate emissions from industry stacks

The anthropogenic emissions are assumed to be 98% by mole SO$_2$ and 2% SO$_4^{2-}$. Since the emissions inventory supplied data at two levels and the height of the interface between the bottom two model levels was generally above 100 m (average height was $\sim$120 m), we apportioned a fraction of the emissions data from above 100 m to the bottom level of the model. The fraction into the bottom level was determined as

$${{zi(1) - 100} \over {zi(2) - 100}},$$

where $zi(1)$ is the height of the top of the lowest level of the model and $zi(2)$ is the height of the top of the second lowest level of the model.

The emissions of DMS were obtained from the biogenic sulfur emissions inventory of [86].

4.12.2 Chemical Reactions

The order of the chemistry calculations is as follows. The aqueous chemistry is performed after the cloud water mixing ratio is determined. The new H$_2$O$_2$, SO$_2$, and SO$_4^{2-}$ concentrations are then used for the gas chemistry calculations. The modified H$_2$O$_2$, SO$_2$, and SO$_4^{2-}$ concentrations then are used in the wet deposition calculation. After the chemistry and wet deposition are calculated, transport through subgrid convective cores is determined for the interstitial fraction of each species (because of their high solubility, sulfate aerosols are not convectively transported). Because a centered time step is used, a time filter couples the concentrations from the odd and even time step integrations. Then the emissions and dry deposition calculations are performed.

The reactions used for the sulfur cycle are described in Table 4.7.

Table 4.7: Reactions Included in the Global Sulfur Model

	$k_{298}$4.1	${E \over R}$	Reference4.2
Gas Chemistry
(R1)	SO$_2$+ OH + M	$\rightarrow$	SO$_4^{2-}$+ M	k$_o$=3.0 $\times 10^{-31}$ $({T \over 300})^{-3.3}$		NASA97
				k$_{\infty}$=1.5 $\times 10^{-12}$
(R2)	DMS + OH	$\rightarrow$	$\alpha$SO$_2$+ (1 - $\alpha$) MSA4.3			Y90
(R3)	DMS + NO$_3$	$\rightarrow$	SO$_2$+ HNO$_3$	1.0 $\times 10^{-12}$	500.	NASA97
(R4)	HO$_2$+ HO$_2$	$\rightarrow$	H$_2$O$_2$+ O$_2$	8.6 $\times 10^{-12}$	-590.	NASA97
(R5)	H$_2$O$_2$+ h$\nu$	$\rightarrow$	2OH	see text
(R6)	H$_2$O$_2$+ OH	$\rightarrow$	HO$_2$+ H$_2$O	1.7 $\times 10^{-12}$	160.	NASA97
Aqueous Chemistry
(R7)	HSO$_3^-$+ H$_2$O$_2$	$\rightarrow$	SO$_4^{2-}$+ 2H$^+$+ H$_2$O	2.7 $\times 10^7$ 4.4	4750.	HC85
(R8)	HSO$_3^-$+ O$_3$	$\rightarrow$	SO$_4^{2-}$+ H$^+$+ O$_2$	3.7 $\times 10^5$	5300.	HC85
(R9)	SO$_3^{2-}$+ O$_3$	$\rightarrow$	SO$_4^{2-}$+ O$_2$	1.5 $\times 10^9$	5280.	HC85
Equilibrium Reactions
(R10)	H$_2$O$_2$(g)	$\rightleftharpoons$	H$_2$O$_2$(aq)	7.4 $\times 10^4$	-6621.	LK86
(R11)	O$_3$(g)	$\rightleftharpoons$	O$_3$(aq)	1.15 $\times 10^{-2}$	-2560.	NBS65
(R12)	SO$_2$(g)	$\rightleftharpoons$	SO$_2$ (aq)	1.23	-3120.	NBS65
(R13)	H$_2$SO$_3$	$\rightleftharpoons$	HSO$_3^-$+ H$^+$	1.3 $\times 10^{-2}$	-2015.	M82
(R14)	HSO$_3^-$	$\rightleftharpoons$	SO$_3^{2-}$+ H$^+$	6.3 $\times 10^{-8}$	-1505.	M82

4.12.2.1 Gas-Phase Reactions

Oxidation of SO$_2$ to form sulfate, oxidation of DMS to form SO$_2$, and production and destruction of H$_2$O$_2$ are represented in the model.

In R1, it is assumed that the SO$_2$ + OH reaction is the rate-limiting step of the multistep process of forming aerosol sulfate. Concentrations of short-lived radicals OH, NO$_3$, and HO$_2$ are prescribed using three-dimensional, monthly averaged concentrations obtained from the Intermediate Model of Global Evolution of Species (IMAGES) [130]. The diurnal variation of these oxidants is not included in our calculations, but instead, the diurnally averaged value is used at each time step. The rate coefficient for (R2) follows Benkovitz et al. [16], who followed the work of Yin et al. [195,194]. The rate of H$_2$O$_2$ photolysis is determined via a look-up table method where the photolysis rate depends on the diurnally averaged zenith angle and the height of the grid point, assuming that the albedo for ultraviolet radiation is 0.3. Because R4 is nonlinear and the diurnally averaged rate of reaction does not equal the reaction rate of diurnally averaged HO$_2$ mixing ratios, the HO$_2$ mixing ratios are adjusted by the amount of daylight at any given latitude. The rates of the sulfur reactions are determined by the effective first-order rate coefficient and using a quasi-steady state approximation [70]. The H$_2$O$_2$ concentration determined from the gas-phase reactions is calculated using an Euler forward approximation.

4.12.2.2 Aqueous-Phase Reactions

Oxidation of aqueous SO$_2$ by O$_3$ and H$_2$O$_2$ to form SO$_4^{2-}$ aerosol is included in the model (Table 4.7). The concentrations of O$_3$ are prescribed using three-dimensional, monthly averaged concentrations obtained from the IMAGES model. Prescribed species (O$_3$, OH, HO$_2$, and NO$_3$) are set according to the linearly interpolated concentration for the location of the grid point and the time of year.

The pH of the drops is determined diagnostically assuming an NH$_4^+$ to SO$_4^{2-}$ molar ratio of 1.0.

$$[H^+] = [HSO_3^-] + [SO_4^{2-}].$$

The liquid water content in a grid cell is determined by combining the resolved-scale cloud water mixing ratio that is predicted, the subgrid-scale deep convective and shallow convective cloud water mixing ratios, and the resolved-scale rain mixing ratio that is diagnosed from the precipitation rate using a mass-weighted fall speed, which is determined assuming a Marshall Palmer size distribution for rain. SO$_2$ and H$_2$O$_2$ are depleted and SO$_4^{2-}$ is produced only in the cloudy region of the grid box. The grid box concentration of these species is found by multiplying the cloudy region concentration times the cloud fraction and the clear air concentration times the fraction of clear air in the grid box.

Because the rate of S(IV) (= SO$_2$ $\cdot$ H$_2$O + HSO$_3^-$ + SO$_4^{2-}$) oxidation by O$_3$ depends on the pH of the drops, the aqueous-phase reactions are evaluated using a 2-min time step with an Euler forward numerical approximation. At the end of each 2-min time step the hydrogen ion concentration is recalculated so that the influence of pH on S(IV) oxidation is captured.

4.12.3 Wet Deposition

The wet deposition rates are calculated separately for gases and aerosols. Cloud water and rain mixing ratios from both the resolved clouds and the subgrid-scale clouds are determined for the cloudy volume in each grid column. Trace gases are scavenged only by the liquid hydrometeors, whereas aerosols can also be scavenged by snow.

The fraction of a trace gas that is in the liquid water is determined through each species' Henry's law coefficient, which is temperature- and/or pH-dependent. At any particular level in the model the flux of the dissolved trace gas in the precipitation entering the grid cell from above is found. The trace gas is reequilibrated with the current model level's properties. Then the flux of the dissolved trace gas exiting the model level is determined. The rate of wet deposition is found from the flux divergence, maintaining mass conservation.

The wet deposition of aerosols is performed in a similar flux method. Any layer in the model can undergo both below-cloud and in-cloud scavenging.

The below-cloud scavenging follows Dana and Hales [47] and Balkanski et al. [10]. It is assumed that both rain and snow, which has graupel-like characteristics (and therefore characteristics similar to rain), scavenge the aerosol below cloud. Removal is assumed to take place by a first-order loss process. That is,

$$L_{W,bc} = 0.1P q$$

where $L_{W,bc}$ is the loss rate by below-cloud scavenging, 0.1 is the collection efficiency, $P$ is the precipitation flux expressed in mm h$^{-1}$, and $q$ is the species mass mixing ratio.

In-cloud scavenging is performed assuming that the some fraction (currently 30%) of the aerosol reside in the cloud water. That fraction is then removed in proportion to the fraction of cloud water that is converted to rain through coalescence and accretion processes. This fraction of the aerosol is removed through wet deposition.

Evaporation of rain is accounted for in the wet deposition rate calculation by releasing a proportionate mass of aerosol to the atmosphere (i.e., if 10% of the precipitation evaporates, then 10% of the sulfate aerosol is released back to the air). This last assumption could lead to an overestimate of sulfate mixing ratios in the air [11] because the number of drops that completely evaporate (and therefore the amount of sulfate aerosol released from the drop to the air) is not necessarily proportional to the mass of rain that evaporates.

4.12.4 Dry Deposition

In [12] we used of dry deposition similar to that described by Benkovitz et al. [16]. The deposition velocity of SO$_2$ is determined following the series resistance method outlined by Wesely [180] where the deposition velocity is inversely proportional to the sum of the aerodynamic resistance, the resistance to transport across the atmospheric sublayer in contact with surface elements, and the surface resistance. The aerodynamic and sublayer resistances are determined using boundary layer meteorological parameters. The surface resistance is found through a parameterization outlined by Wesely [180].

We are in the process of integrating this calculation with the surface process characterization produced by the Common Land Model (CLM). When complete, the internal consistency of the parameterization will be much improved.

In the meantime, we have chosen to prescribe our deposition velocities following [58]. For SO$_2$ we use 0.6 cm/s for land, 0.8 cm/s over ocean, and 0.1 cm/s over ice and snow. Deposition velocities for SO$_4^{2-}$ are set to 0.2cm/s everywhere.