In the case of aerosol particles, the fraction incorporated in the condensed phase depends on aerosol and cloud microphysics in a complex way. It is sometimes assumed that ki ≈ k, meaning that all aerosol is in the condensed phase. A distinction is often made between hydrophobic and hygroscopic aerosol, and more sophisticated treatments can be used in models that resolve the aerosol size distribution (Seinfeld and Pandis, 2006).
In the case of gases and for a warm cloud, the fraction fi,L present in the liquid phase is determined by the effective Henry’s law constant [M atm–1] (see Section 5.5.1):
(8.136)
where L is the cloud liquid water content [m3 water per m3 air], T is the temperature [K], and is the ideal gas constant. For a typical precipitating cloud with L ~ 1 × 10–6, gases with ≫ 104 M atm–1 are efficiently scavenged (fi,L → 1) while gases with ≪ 104 M atm–1 are not scavenged (fi,L → 0). Gases can also be taken up by ice crystals in mixed or cold clouds. The fraction fi,I present in the ice phase can be estimated from a surface coverage model (such as a Langmuir isotherm) or a co-condensation model (Mari et al., 2000).
8.9.2 Rainout and Washout
Scavenging outside convective updrafts, including in-cloud scavenging (rainout) and below-cloud scavenging (washout), can be treated as a first-order loss process in the precipitating column. For each grid column the meteorological model must provide information on the vertical distribution of precipitation rates. Let Pj represent the precipitation rate [cm water s–1] through the bottom of model level j. One must apply rainout to the in-cloud levels where new precipitation forms (Pj > Pj + 1) and washout to the below-cloud levels where precipitation evaporates (Pj ≤ Pj +1). We start the scavenging calculation at the top of each precipitating column and progress downward level by level, applying rainout or washout/reevaporation as appropriate.
Rainout can be computed similarly to scavenging in the convective updrafts described in Section 8.9.1. The fraction Fi of species i scavenged from a grid cell over a time step Δt is given by
Fi = fA(1 − exp [−kiΔt])
(8.137)
where fA is the areal fraction of the grid cell experiencing precipitation and ki [s–1] is a first-order rainout rate constant. From knowledge of the rainout rate constant k of the condensed water in the cloud, we can calculate ki in the same manner as in the case of convective updrafts (8.134). Values of fA and k may be supplied as part of the hydrological information from the driving meteorological model. If not, they need to be estimated, and classic parameterizations for this purpose are available from Giorgi and Chameides (1986) and Balkanski et al. (1993). Accounting for fA < 1 when precipitation is subgrid in scale is important because scavenging of water-soluble species from a precipitating column is highly efficient. Assuming fA = 1 would lead to an overestimate of scavenging.
Washout involves the below-cloud uptake of aerosol particles and gases by hydrometeors (raindrops or ice crystals). For aerosol particles and highly soluble gases, washout is a kinetic process limited by mass transfer (collision rates for particles, molecular diffusion for soluble gases). The scavenged fraction Fi of species i for a grid cell experiencing washout over a time step Δt is given by:
(8.138)
where ki′ [cm–1] is a first-order washout rate constant, typically ~1 cm–1 for aerosol particles and highly soluble gases. Parameterizations for ki′ are given for example by Feng (2007, 2009) for scavenging of aerosol particles by rain and snowfall, and by Levine and Schwartz (1982) for scavenging of highly soluble gases by rain. Evaporation of precipitation below cloud will not release these species to the surrounding air if the hydrometeors simply shrink; evaporation must be complete. In the case of partial evaporation, one must make an assumption about the fraction of hydrometeors that shrink and the fraction that evaporate entirely. A 50/50 assumption is often made.
For moderately soluble gases where washout is not limited by mass transfer, we can assume equilibrium between the hydrometeors and the surrounding air within the precipitating fraction of the grid cell. In that case, the fraction of species i that is incorporated in the liquid or ice can be calculated using fi,L and fi,I as given in Section 8.9.1 for the case of convective updrafts. In particular, fi,L is given by:
(8.139)
where LP is the rainwater content of the precipitating fraction of the grid cell defined as the volume of precipitation to which a unit volume of air is exposed over timestep Δt:
(8.140)
This equilibrium treatment allows for evaporative release of gases below cloud level to respond directly to the downward decrease of Pj from level to level. Let mj represent the mass of a species i in grid cell j and Δmj+1 represent the mass scavenged into the grid cell through the top over time Δt by precipitation overhead. The mass Δmj transported out through the bottom of the grid cell by precipitation over time Δt is then given by:
Δmj = fi(fAmj + Δmj + 1)
(8.141)
8.10 Lightning and NOx Production
Deep convective storms with strong updrafts generate lightning as a result of electrical charge separation between the cloud and the surface. Heating in the lightning bolt produces a plasma with temperatures exceeding 106 K. This leads to the production of nitric oxide (NO) from air molecules, initiated by thermolysis of O2 (Zel’dovich mechanism):
(8.142)
Estimates for the global source of NOx from lightning range from 1 to 20 Tg N a–1 (Schumann and Huntrieser, 2007), which can be compared to a global NOx source from fossil fuel combustion of about 30 Tg N a–1. Lightning releases NOx in the upper troposphere, where it is particularly efficient for producing ozone and OH. As such, it plays a major role in determining tropospheric oxidant levels.
Figure 8.13 shows the global climatological distribution of lightning observed from space. Lightning mainly occurs over land where intense heating of the ground leads to strong convective updrafts. Lightning NOx is mostly released in the detrainment zone at the top of the updraft (Ott et al., 2010). Active nonlinear chemistry producing ozone takes place in this detrainment ozone as lightning NOx interacts with water vapor and VOCs injected in the updraft.
Figure 8.13 Climatological distribution of lightning flashes [flashes km–2 a–1] for different seasons based on observations by the Optical Transient Detector (OTD).
From Christian et al. (2003).
The standard way to represent the lightning source of NOx in models is as part of the parameterization for convective transport, thus ensuring that the association between lightning NOx and convective outflow driving nonlinear chemistry is captured. The lightning flash rate in the convective column is parameterized on the basis of the strength and/or depth of the convection, and a NOx yield per flash is assumed that may vary depending on the energy of the flash. Some models distinguish between cloud-to-ground and intra-cloud flashes in that regard.
Different model parameterizations have been proposed to compute lightning flash rates in deep convection. Cloud-resolving models use the convective updraft velocity as the best predictor variable, but this variable is generally not available in coarser-resolution models. A common parameterization for global models is that of Price and Rind (1992), which expresses the flash frequency F [flashes per minute] as a steep function of the cloud top height H [km], with separate expressions for continental (c) and maritime (m) convection:
Fc = 3.44 × 10−5H4.9 Fm = 6.4 × 10−4H1.73
(8.143)
Other parameterizations relate lightning flash frequency to deep convective mass fluxes (Allen et al., 2000) or to convective precipitation (Meijer et al., 2001). None of these parameterizations have much success in reproducing lightning observations (Murray et al., 2012). Models for the present-day atmosphere can constrain the distribution of lightning flash frequencies with satellite and ground-based observations, and apply these locally or regionally to the deep convective updrafts simulated by the model (Sauvage et al., 2007; Murray et al., 2012). This offers a more realistic representation of present-day ligh
tning but it cannot be used to simulate past or future climates.
Estimates of NOx yields from lightning flashes span a wide range from 30 to 1000 moles per flash (Price et al., 1997; Théry et al., 2000; Schumann and Huntrieser, 2007). Yields depend on the energy of the flash, but this is very poorly constrained. The general practice in atmospheric models is to adjust the global lightning NOx source to a value that is compatible with observed atmospheric concentrations of reactive nitrogen oxides (NOy, including NOx and its oxidation products) and tropospheric ozone. This leads to a global source in the range 2–8 Tg N a–1 (Solomon et al., 2007). The implied NOx yields per flash are in the range 200–500 moles, consistent with atmospheric observations (Murray et al., 2012).
8.11 Gravity Waves
Gravity waves are oscillations that develop in stably stratified air when air parcels are displaced vertically, for example by mountain ranges or by neighboring thunderstorms. Their horizontal wavelengths are typically ~10–100 km. The vertical propagation of these waves depends on the vertical profile of the mean horizontal wind speed; waves are absorbed at a critical level where the phase speed c of the wave is equal to the mean wind speed u. As the waves propagate vertically, their amplitude increases as the inverse of the air density. The perturbation of temperature in the mesosphere or lower thermosphere becomes so large that the air becomes convectively unstable and the waves break (Figure 8.14, a). The momentum transported by the wave from lower atmospheric levels is transferred to the mean flow, which leads to an attenuation of the zonal flow and triggers a meridional circulation directed from the summer to the winter hemisphere (Figure 8.14, b). Vertical mixing also takes place.
Figure 8.14 (a) Two-dimensional model of the potential temperature field (isentropes) perturbed by a prescribed gravity wave source located at the triangle along the x-axis. The figure shows the propagation of the gravity wave after 160 minutes of model integration, i.e., at a mature stage of wave breaking. Reproduced from Prusa et al. (1996). Copyright © American Meteorological Society, used with permission. (b) Global distribution of wind acceleration [m s–1 d–1] in the upper atmosphere as driven by gravity wave breaking above 70 km altitude. The resulting global mean meridional circulation, schematically represented by arrows, is characterized by upward (downward) motions in the summer (winter) hemisphere.
Reproduced from Brasseur and Solomon (2005).
Gravity waves cannot be explicitly represented at the grid resolution of global models and their effects must therefore be parameterized. Different formulations have been proposed (Lindzen, 1981; Medvedev and Klaassen, 1995; Hines, 1997a, 1997b). In a very simple approach, Lindzen (1981) derives the gravity wave drag (G) and vertical eddy diffusion coefficient (Kz) from the following expressions:
(8.144)
(8.145)
where k is the horizontal wavenumber of the wave, H is the atmospheric scale height, and N is the Brunt–Väisälä frequency (N2 = g ∂lnθ/∂z if θ is the potential temperature and z the altitude). In most parameterizations, rather than considering the propagation of a single gravity wave, a spectrum of waves with different phase velocities is considered.
8.12 Dynamical Barriers
As discussed in Chapter 2, dynamical barriers in the atmosphere limit the rate at which mass is exchanged between different atmospheric regions. Transport across these barriers often involves subgrid processes. An important case is the tropopause, where a strong inversion severely restricts transport. Long-lived species penetrate the stratosphere in regions of tropical upwelling. Water vapor is trapped during this transport by condensation and precipitation at the cold temperatures of the tropopause. Downward transport across the tropopause occurs mostly as small-scale tongues of air (tropopause folds) that form in connection with meteorological disturbances. These tongues may eventually mix in the troposphere. Diffusive numerical transport schemes can lead to spurious fluxes across the tropopause because vertical gradients are particularly large.
Dynamical barriers also restrict meridional transport in the stratosphere. The sub-tropical barrier isolates tropical rising air (the tropical pipe) from mid-latitude influences. A second barrier arises from the two polar vortices that isolate polar regions from lower latitudes. Transport through these barriers involves dynamical disturbances at scales that are generally unresolved by models. For example, narrow filaments are stripped away from the polar vortex in response to planetary wave breaking events. These very thin structures are stretched around the vortex before they mix with the surrounding air masses.
The need to resolve dynamical barriers has motivated the development of Lagrangian models of stratospheric transport (Fairlie et al., 1999). These Lagrangian models describe the deformation and dissipation of the filaments on the basis of the flow divergence (McKenna et al. 2002). Comparisons to observations show that the Lagrangian models are far more effective than their Eulerian counterparts in generating and preserving the filamentary structures.
8.13 Free Tropospheric Plumes
The free troposphere, ranging from the top of the boundary layer (~2 km) to the tropopause, is on average a convectively stable environment. Observations show that chemical plumes injected into the free troposphere by convection, volcanoes, or stratospheric intrusions can retain their identity as well-defined layers for a week or more as they are transported on intercontinental scales. Vertical soundings of the free troposphere often reveal the presence of distinct chemical layers, typically ~1 km thick and stretching horizontally in filaments spread over ~1,000 km (Thouret et al., 2000; Heald et al., 2003). Global Eulerian models have great difficulty in reproducing such layered structures in the free troposphere. The plumes dissipate much too quickly, even when they are sufficiently thick that they should be resolved at the model grid scale. This problem is very different in nature from the turbulent diffusion of boundary layer plumes emitted from point sources, typically simulated with a Gaussian plume or puff model (Section 4.12). Boundary layer plumes dissipate on a timescale of hours, but free tropospheric layers persist for considerably longer because of the convectively stable environment.
Figure 8.15 from Rastigejev et al. (2010) illustrates the problem. It shows the transport over nine days of an inert chemical in a 2-D (horizontal) model of the free troposphere over the Pacific. The model has 2°×2.5° horizontal resolution. The chemical is released uniformly at t = 0 over a 12°×15° domain, resolved by 6 × 6 grid squares. Transport is solely by advection, computed with a second-order accurate piecewise parabolic scheme. The advection equation should perfectly conserve the mixing ratio in the plume, but the model plume is instead rapidly dissipated. The bottom panel of Figure 8.15 shows the decay of the maximum mixing ratio in the plume with time. After two days the maximum mixing ratio has dropped to 40% of the initial value; after one week it is less than 10%. As shown in Figure 8.15, this fast numerical decay of the plume is caused by the strong variability of the atmospheric flow. A simulation using the same model with uniform flow shows only 10% dissipation in two weeks, reflecting the high-order accuracy of the advection scheme. Introducing a convergent–divergent pattern in this uniform flow causes a sharp increase in plume dissipation.
Figure 8.15 Free tropospheric advection of a chemically inert plume in a 2-D version of the GEOS-Chem chemical transport model with 2°×2.5° horizontal resolution. The plume is released at time t = 0 as a uniform layer over a 12°×15° domain. (a) Shows the evolution of plume mixing ratios over nine days in a variable atmospheric flow at 4 km altitude from the NASA GEOS meteorological data assimilation. (b) Shows the decay of peak mixing ratios in the plume for the atmospheric flow of the left panel, for a uniform flow, and for a uniform flow with convergent–divergent perturbation applied between 125 and 200 h.
From Rastigejev et al. (2010).
Plume dissipation in variable flow as illustrated by Figure 8.15 is due to divergence of the wind, causing stretching of the plume. The divergence is measured by the Lyapunov exponent λ, defined as the exponential rate at which ne
arby trajectories diverge from each other: λ = ∂u/∂x where u is the wind speed in the direction x of the flow. In the absence of molecular diffusion, the continuity equation prescribes that the chemical concentration within the plume should remain constant in time even with stretching. However, numerical diffusion in the advection algorithm causes the plume to decay rapidly when stretched. We represent the numerical diffusion by a diffusivity D normal to the flow. In this conceptual 2-D example the diffusion is taken to be horizontal; but the same argument applies to diffusion in the vertical. To estimate the rate of decay, we need to know the characteristic length scale over which the concentration decays at the edge of the plume. This length scale rb is determined by a balance between diffusion and stretching. Intuitively, if the plume is very thick, stretching dominates and the plume filaments; conversely, if the plume is very thin, diffusion dominates and the plume thickens. There is an equilibrium thickness for which diffusion and stretching are in balance. The rate constant for diffusion is , while the rate constant for stretching is λ. Balance between diffusion and stretching thus implies
(8.146)
If we assume that the mixing ratio μ of the chemical species is uniform in the plume and zero in the surrounding background, then the rate of decay of μ is given by the diffusive outflux through the boundary, namely
(8.147)
where V and S are the volume and surface area of the plume. Now V/S = W, the width of the plume in the direction perpendicular to the stretching direction of the flow. Hence the mixing ratio in the plume decays exponentially as μ ∼ exp [-αt], with
Modeling of Atmospheric Chemistry Page 47