9.3.7 Factors Controlling the Dry Deposition Velocity
The deposition velocity of a gas as described by the resistance-in-series model (9.26) can be limited by aerodynamic transfer if RA ≫ RC,i or by surface uptake if RA ≪ RC,i. It is never limited by transfer in the quasi-laminar boundary layer because RA ≫ RB,i in all cases. Whether aerodynamic transfer or surface uptake is limiting depends on species properties, canopy properties, and atmospheric stability. Gases with weak surface reactivity have low deposition velocities generally limited by the surface resistance. At the other extreme, strong acids like HNO3 have zero surface resistance and their deposition velocity is always limited by aerodynamic transfer. Aerosol particles have highly variable deposition velocities depending on their size and on the canopy structure. Deposition velocities are smallest for particles in the 0.1–1 μm range. Smaller particles are efficiently removed by Brownian diffusion, while larger particles are efficiently removed by inertial impaction.
Deposition velocities over land vary strongly between day and night as driven both by atmospheric stability and by surface resistance (Table 9.3). This is illustrated in Figure 9.16 with measured ozone deposition velocities above a forest canopy. The deposition velocity is low at night when the atmosphere is stable and the stomata are closed. It increases rapidly at sunrise when the stomata start to open, and peaks in midday when the stomata are most open and the atmosphere is unstable. A mean afternoon decline in dry deposition is often observed due to increasing cloudiness resulting in partial stomatal closure. Also shown in Figure 9.16 are model values computed with a standard big-leaf resistance-in-series scheme and including variability driven by temperature and solar radiation.
Figure 9.16 Diurnal variation of the ozone dry deposition velocity over a pine forest in North Carolina, April 15 to May 15, 1996. Mean observations and standard errors from Finkelstein et al. (2000) are compared to mean values from the GEOS-Chem model using a resistance-in-series parameterization. Model standard deviations describing day-to-day variability are also shown.
From Katherine Travis, Harvard, personal communication.
Figure 9.17 illustrates the geographical and seasonal variations in ozone dry deposition velocity as calculated from a global model. Values are much lower over ocean than over land because ozone is poorly soluble in water. Values are also much lower in winter than in summer due to the absence of a leaf canopy and the suppression of deposition by snow.
Figure 9.17 Monthly mean ozone deposition velocity [cm s–1] in January and July calculated in the model of Lamarque et al. (2010).
9.3.8 Gravitational Settling
Gravitational settling is an important contributor to the deposition velocity in surface air only for aerosol particles larger than about 10 μm. The gravitational settling velocity near the Earth’s surface is of the order of 1 cm s–1 for a 10 μm particle and 0.01 cm s–1 for a 1 μm particle. Gravitational settling is more important in the free troposphere and stratosphere, where vertical motions are otherwise slow and the settling velocity is higher than in surface air because of lower atmospheric pressure. Because of this, it is important to add gravitational settling as a term in the continuity equation for particles larger than about 1 μm (Chapter 4). Here we present equations for the gravitational settling velocity of particles that are applicable both for computing deposition at the surface and vertical motion through the atmosphere.
The settling velocity w of a particle of mass mp is determined by equilibrium between gravity and drag:
(9.33)
The drag is given by:
(9.34)
where ap is the projected area of the particle normal to the flow, ρa is the air density, and CD is an empirical drag coefficient. For spherical aerosol particles (ap = π /4):
(9.35)
where Dp is the particle diameter. For particles that are not very large relative to the mean free path of air molecules (λ = 0.065 μm at 298 K and 1 atm, but λ = 0.42 μm at 215 K and 100 hPa in the lower stratosphere), a dimensionless slip-correction factor Cc must be introduced to account for non-continuum effects:
(9.36)
with
(9.37)
This correction factor decreases the drag and therefore increases the settling velocity. The mean free path is computed as
(9.38)
where p is the atmospheric pressure, Ma is the molecular weight of air, is the ideal gas constant, T is the absolute temperature [K], and μ is the dynamic viscosity [kg m–1 s–1] given by
(9.39)
where To = 298 K and μo = 1.8 × 10–5 kg m–1 s–1.
The terminal settling velocity ws of a particle, obtained from equilibrium between gravity and drag (dw/dt = 0 in (9.33) is given by
(9.40)
where ρp is the mass density of the particle. The drag is a function of the Reynolds number Re:
(9.41)
For near-surface conditions (1 atm and 298 K), the Reynolds number is less than 0.1 for Dp smaller than 20 μm. Under low Reynolds numbers (Re < 0.1), the drag coefficient can be expressed as CD = 24/Re, and ws is then given by
(9.42)
At higher Reynolds numbers the following equations for the drag apply:
(9.43)
The terminal settling velocity must then be calculated iteratively using (9.40) and (9.43) to account for the dependence of CD on Re, and hence ws.
Figure 9.18 shows typical gravitational settling velocities as a function of particle size and compares these velocities to measurements of particle dry deposition velocity to a grass surface. Gravitational settling accounts for 10% of the overall deposition velocity for 1 μm particles and 20% for 10 μm particles (typical of fog). Even though the gravitational settling velocity increases by two orders of magnitude from 1 to 10 μm, removal by inertial impaction also becomes more efficient. Gravitational settling dominates deposition for particles larger than 30 μm (for context, the diameter of a small raindrop is 100 μm).
Figure 9.18 Curve A: Gravitational settling velocity of aerosol particles as a function of particle diameter. Curve B: Deposition velocity of aerosol particles onto a grass surface.
From Hobbs (2000).
9.4 Two-Way Surface Flux
The one-way deposition model described in Section 9.3 assumes that the surface is a terminal sink for depositing species. This assumption is expressed in the big-leaf model by the boundary condition of a zero concentration in the surface reservoir (Figure 9.14 and equation (9.24)). Consider instead as boundary concentration a non-zero concentration ni,o in the surface reservoir. Equation (9.24) then becomes
(9.44)
Combining (9.21), (9.23), and (9.44) yields:
FD, i = − wD, i[ni(z1) − ni, o]
(9.45)
We see that a non-zero concentration within the surface reservoir (called a compensation point) implies a surface emission flux wD,i ni,o offsetting the deposition flux –wD,i ni(z1). The emission is subject to the same resistances to transfer as deposition. wD,i is then called a transfer velocity, exchange velocity, or piston velocity rather than a deposition velocity.
Proper representation of the non-zero compensation point in an atmospheric model depends on the nature of the source that maintains this compensation point. If the source is atmospheric deposition, this means that reaction within the surface reservoir is not sufficiently fast for the surface to be a terminal sink; re-emission to the atmosphere is a competing pathway. In that case, ni,o is dependent on ni(z1), and a relationship between the two must be specified. This may be as simple as assuming a fixed proportionality, e.g., ni,o = sKni(z1) where K is an equilibrium constant between the surface reservoir and the atmosphere (such as Henry’s law for an air–water interface) and s is a saturation ratio. Or it may be as complex as a full biogeochemical model for the surface reservoir in which the gross deposition flux –wD,ini(z1) is an input and the surface emission flux wD,ini,o is an output. The atmospheric model must then be coupled to the biogeochemical model.
Frequently
, however, the compensation point can be considered to be independent of atmospheric deposition. This occurs when production within the surface reservoir dominates over the supply from atmospheric deposition. In such cases, the gross deposition flux –wD,i ni(z1) and the surface emission flux wD,i ni,o are decoupled: the gross deposition flux is determined by the atmospheric concentration while the emission flux is not, so they are best computed and diagnosed as separate quantities. The surface concentration ni,o may be specified from observations or computed with a biogeochemical model for the surface reservoir. The gross deposition flux is the relevant sink to the surface from the perspective of the atmospheric budget, and the surface emission flux is the relevant source.
In the calculation of two-way exchange by (9.45), the same exchange velocity wD,i is used to compute gross deposition –wD,ini(z1) and surface emission wD,ini,o. This reflects the conservation of the vertical flux between z1 and the point in the surface reservoir where the concentration ni,o is specified. The resistance-in-series model described in Section 9.3 for one-way deposition can thus be adapted to two-way exchange simply by specifying a non-zero ni,o at the surface reservoir endpoint. For example, the formulation of RC,i in Figure 9.15 includes three surface reservoir endpoints: inside the leaf mesophyll, at the lower canopy surface, and at the ground surface. In the one-way deposition model, concentrations at these endpoints are taken to be zero. Two-way exchange can be simulated by substituting non-zero values. A non-zero concentration is often specified in the leaf mesophyll to represent emission from leaves.
A common application of two-way surface exchange is the two-film model for the air–sea interface (Liss, 1973). In this case, the two-way exchange problem is relatively well posed. A single endpoint concentration ni,o in the bulk near-surface seawater can be specified from ship observations or from an ocean biogeochemistry model. The air–sea equilibrium is characterized by Henry’s law. Transfer across the air–sea interface can be characterized by two resistances in series, one for the gas phase and one for the water phase. The two-film model as generally formulated in the literature follows standard conventions from the oceanography community. Thus vertical transfer in the gas and water phases is measured by conductances kG,I and kW,i that are the inverse of resistances, and the Henry’s law equilibrium constant Hi is defined as the dimensionless ratio of air to water concentrations (in contrast, atmospheric chemists generally define the Henry’s law constant as the ratio of water to air concentrations in units of M atm–1).
Figure 9.19 is a schematic of the two-film model. Conservation of the vertical flux Fi is assumed between the lowest atmospheric model point z1 and the bulk water phase where a concentration ni,o is specified:
Fi = kG, i[nG, i(0) − nG, i(z1)] = kW, i[ni, o − nW, i(0)]
(9.46)
where nG,i and nW,i refer to the concentrations in the gas and water phases respectively. Application of the effective Henry’s law constant Hi = nG,i(0)/nW,i(0) at the air–sea interface allows us to express the flux in terms of bulk concentrations only:
Fi = Ki[Hi ni, o − nG, i(z1)]
(9.47)
where Ki [cm s–1] is the air–sea exchange velocity obtained by adding the gas-phase and water-phase conductances in parallel:
(9.48)
Figure 9.19 Two-film model for air–sea exchange.
The marine atmosphere has near-neutral stability with a roughness height determined by wind-driven waves. It follows that turbulent mass transfer can be parameterized as a function of wind speed only, and the wind at 10-m height (u10) is used for that purpose. Molecular diffusion at the interface depends on the Schmidt number Sci, which is different in the air and water phases. Johnson (2010) gives a detailed review of different parameterizations for kG,I and kW,i, shown in Figure 9.20 as a function of wind speed. A simple expression for kG,I is that of Duce et al. (1991):
(9.49)
where kG,I and u10 have the same units [m s–1] and Mi is the molecular weight in [g mol–1]. On the water side, the parameterization of Nightingale et al. (2000) is often used:
(9.50)
where kW,i is in units of [cm h–1], u10 is in units of [m s–1], and the Schmidt number in water (ScW,I) has been normalized to that of CO2 (ScW,CO2 = 600).
Figure 9.20 Gas-phase and water-phase conductances in the two-film model for air–sea exchange as a function of 10-m wind speed. (a) Different parameterizations of kG,I for air–sea exchange of O2 and CHI3. (b) Different parameterizations of kW,i for a species with Schmidt number in water ScW,I = 660. Different parameterizations can differ by more than a factor of 2 for a given wind speed and this reflects current uncertainty.
Adapted from Johnson (2010).
We see from (9.48) that the overall exchange velocity Ki can be limited by transfer either in the gas or in the water phase depending on the relative magnitudes of Hi and kW,i/kG,i. Table 9.4 gives values of Hi for a few species in pure water at 298 K; Johnson (2010) gives an exhaustive list. Values for seawater are typically 20% lower than for pure water. Assuming as an example a typical wind speed u10 = 5 m s–1 and the molecular diffusion properties of CO2, we derive from (9.49) and (9.50) kG,i = 0.6 cm s–1 and kW,i = 0.002 cm s–1. For highly water-soluble species with Hi < 10–3, such as H2O2, the exchange velocity is limited by transfer in the gas phase and Ki ≈ kG,i. For sparingly water-soluble species with Hi > 10 such as CO2, the exchange velocity is limited by transfer in the water phase and Ki ≈ kW,i/Hi. Gases of intermediate solubility such as methanol or acetone are in a transition regime where exchange is limited by transfer in both the gas and water phases. Hi increases with temperature for all gases, so that the ocean may be a net sink for gases of intermediate solubility at low temperatures and a net source at high temperatures.
Table 9.4 Freshwater Henry’s law constants expressed as dimensionless gas/water concentration ratios
Species Henry’s law constant Hi (dimensionless)
O2 3.2 ×101
CO2 1.2 × 100
Dimethylsulfide 8.2 × 10–2
Acetone 1.4 × 10–3
H2O2 4.6 × 10–6
Figure 9.21 from Fischer et al. (2012) illustrates the two-film model with the net air–sea flux of acetone computed with a global atmospheric model. A fixed seawater acetone concentration of 15 nM is assumed. Acetone in the atmosphere has continental sources (anthropogenic, terrestrial biogenic) and atmospheric sinks (photolysis, oxidation). Net acetone air–sea fluxes are downward at northern mid-latitudes due to relatively high atmospheric concentrations and cold ocean temperatures. They are upward in the tropics due to warm ocean temperatures. They are close to zero at southern mid-latitudes where atmospheric acetone is mostly controlled by a balance between oceanic emission and deposition. On a global scale, there is a close balance in that model between emission of acetone from the ocean (80 Tg a–1) and deposition to the ocean (82 Tg a–1). Even though the ocean is a net sink for acetone, ocean emission accounts for about half of the global acetone source of 150 Tg a–1 and thus plays an important role in controlling atmospheric concentrations.
Figure 9.21 Annual mean net air–sea fluxes of acetone calculated with a global chemical transport model assuming a fixed surface ocean acetone concentration of 15 nM. Circles indicate ship observations.
From Fischer et al. (2012).
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