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Online: http://dust.ess.uci.edu/facts Updated: Sun 25th Jun, 2006, 13:06
Natural Aerosols in the Climate System
by Charlie Zender
University of California at Irvine
Department of Earth System Science zender@uci.edu
University of California Voice:
(949) 824-2987
Irvine, CA 92697-3100 Fax:
(949) 824-3256
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We gratefully acknowledge The Annotated Grateful Dead Lyrics site by David Dodd.
Lyric to “Box of Rain” (p. 169), © Ice Nine Publishing Company. Used with permission.
This monograph describes mathematical, physical, chemical, and computational considerations pertinent to understanding and simulating the distribution and effects of natural aerosols in Earth’s atmosphere. Much of the content applies generically to any aerosol, but the majority of the aerosol-specific sections focus on mineral dust. There are also minor sections on sea salt mobilization and gaseous uptake on sulfate particles.
This monograph benefits from my discussions with many scientists. Their names appear in citations whenever possible. However, many of the their ideas, presented at meetings or in private conversations, are recapitulated here without acknowledgement. These people include Drs. Stephane Alfaro (Université Paris), Richard Arimoto (New Mexico State University), Vicki Grassian (University of Iowa), Zev Levin (Tel Aviv University), Natalie Mahowald (National Center for Atmospheric Research), Bill Nickling (Guelph University), Greg Okin (University of Virgina), Kevin Perry (University of Utah), Yaping Shao (University of New South Wales), and Richard Washington (Oxford University).
Heintzenberg (1989) reviewed the state of knowledge of tropospheric aerosol composition gleaned mainly from boundary layer observations. Gomes et al. (1990) report the observed size distributions and elemental compositions of mineral aerosols measured by a cascade impactor in the Sahara. Alfaro et al. (1997) describe results of wind-tunnel experiments to deduce the dependence of the emitted dust size distribution on the saltation intensity and u*. Prigent et al. (1999) and Lacaze et al. (1999) show how multi-angle and microwave satellite sensors can adequately retrieve land surface properties such as LAI and roughness length, key to determining dust mobilization. Sokolik et al. (1998) show the important role of infrared absorption by mineral dust. Sokolik and Toon (1999) analyze the effects of mineral composition on dust optical properties. Chiapello et al. (1999) compared the in situ observations of mineral dust with TOMS satellite retrievals. Lohmann et al. (1999) counted mineral dust particles smaller than 2 μm as cloud droplet condensation nuclei. Reader et al. (1999a) and Reader et al. (1999b) analyzed changes between mineral dust climatologies during the Last Glacial Maximum and the present. Gillette (1999) describes the factors contributing to the recurrence of dust emission “hot spots” as seen from TOMS. Hamonou et al. (1999) characterize the vertical structure of Saharan dust exported to the Mediterranean basin. Claquin et al. (1999) combined the FAO soil map of the world with surface mineralogy of specific samples to create predictive relationships linking soil type to surface mineralogy on a global scale. Li et al. (1999) showed is it possible to identify specific soil types from as few as six narrow-band infrared measurements. Batt and Peabody II (1999) measured threshold friction velocities for beds of pebbles 5–50 mm in diameter. Ichoku et al. (1999) describe an intensive field campaign in which radiative, microphysical, and chemical properties of various aerosols in the Negev desert were measured and inter-correlated. King et al. (1999) present an overview of the potential of current and future space-borne platforms to measure tropospheric aerosols including dust. Rillig et al. (1999) discovered that the proportion of soil aggregates larger than 250 μm increases linearly with CO2 concentration in certain grasslands due to biological effects. Wang et al. (2000) describe a Kosa (yellow dust) deflation model and evaluations its fidelity over East Asia. Alfaro and Gomes (2001) describe how to estimate the size distribution of the emitted dust by accounting for the size-dependent binding energy of the saltating particles. Arimoto (2001) present a broad overview of the climate factors influencing the abundance of atmospheric dust, as well as the radiative properties controlling the climate impact of dust. Myhre and Stordal (2001) performed sensitivity tests of the global radiative forcing of anthropogenic mineral dust. Grini et al. (2002b) discuss the stability, accuracy, and behavior of sandblasting fluxes determined by the Alfaro and Gomes (2001) model. Lunt and Valdes (2002) develop the Hadley Centre dust model and evaluate it against the standard suite of observations available on Earth. Léon and Legrand (2003) combined visible and infrared satellite measurements to identify dust sources and track dust plumes near the north Indian Ocean. VanCuren (2003) directly measure chemical composition of aerosol, including mineral dust, from Asia which dominates the mass concentration of remote, high altitude sites as far east as the western United States. van Donk et al. (2003) examine anthropogenic erosion on military bases in the Mojave Desert. Kurosaki and Mikami (2003) discovered that increased frequency of strong winds explains much of the observed increased in Dust Storm Frequency (DSF) in East Asia from 2000–2002 relative to the previous decade. Cakmur et al. (2004) show how sub-gridscale gustiness, driven largely dry convection, explains dust emissions in regions where mean winds are otherwise too weak to generate observed emissions. Kurosaki and Mikami (2004) derive an empirical Snow Cover Factor (SCF) that accounts for the influence of snow on the threshold wind velocity for dust mobilization. Grini and Zender (2004) apply show that accounting for saltation, sandblasting, and wind-speed PDFs improves the simulated size distribution of long range transported dust in a global model. Menut et al. (2005) further discuss the problems with determining sandblasting fluxes highlighted by Grini et al. (2002b), and present a new numerically stable scheme for their evaluation. Brooks et al. (2005) describe the interaction between climate and society in the Sahara. Arimoto et al. (2006) summarize dust measurements and modeling during ACE Asia. Many studies examine the possible role of dust as a vector for disease organisms affecting humans (Zender and Talamantes, 2006) and downwind ecosystems such as coral reefs (Shinn et al., 2000; Prospero et al., 2005). Yang et al. (2006) quantify the sensitivity of global dust mobilization, loading, and deposition to assumed size distribution. S. et al. (2006) characterize the effects of iron oxides on dust optical properties.
Many researchers have investigated the Martian dust cycle. In fact, until the 1990s, probably more dust research was performed by researchers more concerned with Mars than Earth. Recent global dust simulations on Mars are described in Pankine and Ingersoll (2002), Newman et al. (2002), and Basu et al. (2004).
Surfaces dissipate the momentum of the wind blowing over them. This dissipation is the result of
tangential shear stress between the wind and the surface elements. The rate of change of atmospheric
momentum Ma
defines a stress force 
and the magnitude of this stress force τ = (
⋅
)1∕2 expresses the
total momentum the surface extracts from the wind per unit surface area per unit time. Hence the surface
wind stress is also called the surface momentum flux. Some fraction of this wind stress τ does work on the
surface in the form of moving the surface elements, e.g., moving leaves, or causing waves. Over
bare or nearly bare ground much of the wind stress must go into aeolian abrasion (over stony
surfaces) or soil movement since there is little else to absorb the force. The remainder of the
wind stress may be converted to frictional heating of the surface, or small scale atmospheric
turbulence.
We define the horizontal wind stress τ by appealing to basic principles of fluid dynamics. A fluid of
density ρ moving at speed U exerts a pressure p (force per unit area) of 
ρU2 on a stationary
object transverse to the flow. The wind stress τ tangential to the surface takes a similar form,
The total stress to the surface 
is the vector sum of individual components representing stress
dissipated by the plant canopy, stress dissipated by airborne (saltating and suspended) particles, and,
finally, wind stress dissipated by the solid surface itself. This stress partition or drag partition has
important implications for dust studies.
Using (2.5) to express the wind stress τ (2.1) solely in terms of u* we obtain
We now consider the wind speed profile U(z) between the free atmosphere and the surface. The planetary surface is the interface between the fluid atmosphere and the “solid” surface (soil, ocean, etc). A solid land surface requires a no slip boundary condition, i.e., the wind speed is zero exactly at the surface. To a good approximation, the ocean may also be treated with the no slip boundary condition since the atmospheric wind speed Ua is usually much larger than the surface current in the ocean uo, i.e., Ua ≫ uo. Let us assume that we know the measured or predicted wind speed Ua at a height z above the surface.
Knowing the wind with speed U at height z exerts a stress τ on the surface,
u* is called the friction velocity, drag velocity, or, more appropriately, the friction speed.Substituting (2.1) into (2.4) we see that
The friction velocity u* is the fundamental quantity determining the flux of dust into the atmosphere. Nevertheless, it is difficult to attach a simple physical interpretation to the friction velocity. However we now demonstrate two important physical properties of u*. First, the mean horizontal wind speed at the top of the laminar layer is u*. Thus immediately after uplift, a particle is embedded in a horizontal wind of speed u*. In §3.3 we use this property of u* to explain the observed cubic dependence of the horizontal mass flux of saltating particles on the wind speed.
Secondly, u* is proportional to the mean velocity gradient 
near the surface.
There are many other useful relations which can be established between U, u*, rm, Cm, and τ. These relations are simple, but tedious, to derive. Table 2.1 lists many of the relations between frequently occurring boundary layer parameters.
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The thermodynamic properties of the boundary layer determine the vertical gradient of fluxes within the boundary layer. In neutral conditions the wind speed varies logarithmically with height according to
where k is the Von Karman constant. The “n” superscript indicates neutral conditions. Strictly speaking, a logarithmic wind profile refers to a wind profile which obeys (2.6). Loosely used, the term refers to any wind profile in the lowest hundred meters or so of the atmosphere. The neutral exchange coefficient for momentum, also called the neutral drag coefficient, is thenFinally, it is sometimes useful to invert (2.7) in order to obtain z0,m in terms of Cn m
The surface fluxes for momentum, heat, and vapor transfer are coupled by micrometeorological exchanges between the surface and the atmosphere in the surface (constant flux) layer. Determination of these fluxes from observation is possible via eddy flux correlation techniques. From a modeling perspective, the fluxes may determined by solving coupled non-linear differential equations in the surface layer. This technique is employed in Large Eddy Simulation (LES) models. LES solution resolve, as exactly as practical, the complex, turbulent eddies which determine the thermodynamic behavior of the boundary layer. However, large scale atmospheric models cannot afford to solve the continuous equations of motions throughout the boundary layer. Instead, a class of bi-level solutions for boundary layer fluxes has been developed based on Monin-Obukhov similarity theory.
Monin-Obukhov similarity theory is usually applied in terms of resistance r and conductance C ≡ r-1 which describe the transfer of scalar quantities between two levels within the boundary layer. For simplicity, one of these levels is taken as zatm the midpoint height of the lowest atmospheric layer in the large scale atmospheric model. A host model provides the potential temperature θatm, pressure patm, specific humidity qatm, and meridional and zonal winds vatm and uatm. The subscript atm indicates the quantities are defined at the height zatm. The momentum fluxes τx and τy [kg m-1 s-2], sensible heat flux H [W m-2], and moisture flux E [kg m-2 s-1] are defined by the vertical gradient of the appropriate thermodynamic quantity between z = zatm and z = zs, where zs is the “surface height” (defined below). The fluxes are expressed as
The similarity of these expressions to one another arises from the definitions of the resistances rm, rh, and rv. These resistances depend implicitly on the fluxes τ, H, and E, through Monin-Obukhov similarity theory. Thus (2.9)–(2.12) must be solved iteratively.Solutions to (2.9)–(2.12) must balance the surface energy budget. In other words, power absorbed by the surface must be dissipated by surface heating/cooling, and energy divergence to the atmosphere or soil in the form of latent, sensible, and radiative heating or cooling.
The turbulent surface fluxes, also called Reynolds fluxes, are the fluxes of heat, moisture, and momentum between the surface and the atmosphere. These fluxes arise as the atmosphere and the surface attempt to reach equilibrium states with the prevailing conditions. Because they are usually unresolved, the turbulent fluxes are usually determined by the application of Monin-Obukhov theory to the prevailing mean conditions. One simple and popular method, the bulk aerodynamic approximation, is of particular utility to large scale atmospheric models. We shall describe the essential physics for determining the turbulent surface fluxes, and related parameters, using the bulk aerodynamic approximation and more complex approximations.
There are three turbulent fluxes of interest: the momentum flux (also called the surface stress or wind
stress) τ [kg m-1 s-2], and the sensible and latent heat fluxes H and L, respectively, both measured in
W m-2. These fluxes are defined in terms of the eddy fluxes of the appropriate fields. Any scalar field
x(t) may be decomposed into time-mean and fluctuating components, 
and x′, respectively
 | =  | (2.14a) |
| x′(t) | = 0 | (2.14b) |
Eddy fluxes arise from the fluctuating components of state variables. Consider the vertical fluxes of the scalar quantity x (2.13). For concreteness, imagine that x represents horizontal wind speed U, temperature T , or specific humidity q. Using (2.13) we see that the instantaneous vertical flux of x is
The time-mean surface flux of x is obtained by applying the time-average operator to (2.16) where we have used the time-mean properties of
and x′ (2.14) and the further property that the vertical
wind vanishes at the surface 
(z = 0) ≡ 0.
The eddy fluxes are multiplied by a pre-factor to obtain the conventional units
| τ | = -ρw′U′ | (2.17a) |
| H | = cpρw′T′ | (2.17b) |
| L | = lρw′q′ | (2.17c) |
The bulk aerodynamic approximation for turbulent fluxes defines the eddy fluxes in terms of the time-mean state variables. The eddy correlations are assumed to be proportional to the product of the horizontal wind speed U and change of the appropriate state variable (U, θ, or q) between the surface and the height of interest.
| -w′U′ | = C mUΔU = CmU2 | (2.18a) |
| w′T′ | = C hUΔθ | (2.18b) |
| w′q′ | = C vUΔq | (2.18c) |
Combining (2.17) with (2.18) we obtain
 | (2.19) |
Each of the variables in (2.19) is height dependent. However, it is very common to evaluate the exchange coefficients at a particular height known as the reference height zr. The reference height is usually taken to be 10 m. Shifting the exchange coefficients between zr an arbitrary height z is useful for putting measurements from a variety of heights into a common framework for analysis.
Table 2.2 describes the defining relations of many of the related quantities which prove useful in boundary layer meteorology.
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Garratt (1977) reviews drag coefficient terminology, relationships, measurements, and constraints.
We assume aerosol has the same flux properties in the boundary layer as momentum. The roughness length for momentum transfer z0,m is a property of the surface characteristics only, i.e., z0,m is independent of wind speed when the following conditions are met:
Rougher surfaces tend to absorb more wind stress into non-erodible elements. Thus saltation decreases as z0,m increases, and visa versa. The frequency of saltation events follows the same pattern, since smooth surface initiate saltation more readily.
Raupach (1994) derived simple analytic relations for the roughness length z0,m and the zero-plane displacement D of vegetated surfaces as functions of vegetation height h and area index Λ. Microwave radar data may be inverted to obtain high resolution roughness length (and soil moisture) data of bare ground globally (e.g., Prigent et al., 1999; Lacaze et al., 1999; Zribi and Dechambre, 2003).
There are two roughness lengths pertinent to wind erosion over bare ground. The first is the aerodynamic roughness length of the bare ground including the non-erodible elements such as pebbles, rocks, and vegetation. This is what is traditionally known as the roughness length for momentum transfer, z0,m. The second roughness length is the so-called “smooth” roughness length, zs 0,m (Marticorena and Bergametti, 1995). zs 0,m is the roughness length of a bed of potentially erodible particles without any non-erodible elements. The roughness length most easily measured in laboratory wind tunnel experiments is zs 0,m. Wind tunnel experiments over uniform beds comprised of known particle sizes show that
However, uniform beds of purely erodible particles are rare in Nature.It is useful to distinguish between the susceptibility of soil to erosion, called erodibility, from the power of the wind (or some other force) to cause erosion, called erosivity. Erodibility depends on the microphysical, chemical, and mechanical properties of the the soil, vegetation, and topography (D’Odorico et al., 2001). Erosivity depends on the wind speed, intermittency, shear, and turbulence.
Discounting erodible particles which are sheltered by non-erodible elements, the roughness length felt by the atmosphere over erodible particles is zs 0,m. Moreover, our theoretical understanding of threshold wind velocities is based on zs 0,m, while most large scale atmospheric models are concerned with total momentum flux, and thus tend to compute z0,m. Thus a theory is necessary to connect the zs 0,m to z0,m. This is the theory of drag partition. The increase fd in threshold friction velocity for saltation u*t due to drag partition is (Marticorena and Bergametti, 1995)
The inverse of fd is the fraction of momentum transferred that is available for inducing saltation, called the wind friction efficiency, fe = fd-1. The roughness lengths z 0,m and zs 0,m are properties of the surface characteristics only, i.e., they are independent of wind speed so long as the surface is not in motion. Gillette et al. (1998) present corrections to this assumption for saltating surfaces.Strong saltation can modify z0,m because the saltators provide a sink for momentum distinct from the surface. Consider a saltator ejected from the surface with an initial speed proportional to u*. It is common assumption that, after launching, a saltating particle experiences no vertical acceleration except gravity. Such trajectories are called ballistic. In a ballistic trajectory, the vertical velocity decreases linearly with time, and the initial upwards velocity equals the final downwards velocity. It is easy to show the height reached by a ballistic saltator is proportional to u*2∕g. Strong saltation causes an effective thickening of the roughness length also in proportion to u*2∕g. For strongly saltating surfaces with u * ≫ u*t, Chamberlain (1983) suggests
For moderate wind friction speeds u* ~ u*t, such effects may be neglected (Leys and Raupach, 1991).Table 2.3 shows typical roughness lengths of non-vegetated surface types.
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The roughness length of fluids depends on the surface wind shear. The shear stress deforms the fluid and generate ripples or waves at higher wind speeds. These waves, in turn, modify the surface roughness length. Chamberlain (1983) pointed out that, in certain circumstances, wind drag entrains very similar amounts of surface mass into the atmosphere over many different surface types. He assembled a variety of observational data which showed that saltation of sand and snow was analogous to entrainment of sea-spray over the ocean. This agreement could be explained by assuming z0,m was proportional to u*2∕g over each of the surfaces. Over oceans, we adopt the dependence of z0,m on U proposed by Large and Pond (1982)
The reference height zr is the height at which the neutral exchange coefficient Cn m is determined. In theory this could be any height but in practice Cn m is measured and parameterized as a function of the wind speed at 10 m (e.g., Large and Pond, 1981; NCAR Oceanography Section, 1997; Bryan et al., 1997). Thus we use U10 instead of Ur. The constraint that U10 > 1 m s-1 prevents surface exchanges from vanishing at small wind speeds.Note that Cn m (2.28) is the not the drag coefficient but is the neutral drag coefficient. Stability-based corrections must be applied to Cn m in order to obtain Cm. Large and Pond (1981) summarize the procedure used to convert Cn m to a (non-neutral) drag coefficient, shifted to any height z:
When z = zr, then Cm is the drag coefficient at the reference height.Exchange coefficients such as the drag coefficient Cm (2.29) are positive-definite by definition, e.g., (2.1). Some care must be taken to ensure numerical procedures do not erroneously predict negative-valued exchange coefficients. For example, (2.29) predicts Cm(z) < 0 when . . . fxm
As mentioned above, the vertical profile of momentum in the boundary layer is, to a first approximation, logarithmic with height (2.6). However, the stability properties of the atmosphere introduce a correction
![[ ( ) ( ) ( )]
U (z ) - U(z ) = u*- ln z2 --D- - ψ z2---D- + ψ z1 --D- (2.30 )
2 1 k z1 - D m L m L](aer46x.png)
The stability parameter ζ is the ratio of the height z to the Monin-Obukhov length L [m] (defined below).
The stability parameter is the non-dimensionalized height in the surface turbulence equations.In the surface layer, the stability parameter equals the flux R
![[ ( )] -2
n 2 z---D-
C m(z,z0,m + D) = k ln z0,m (2.7 )](aer24x.png)
![w(t)x(t) = [ˉw + w ′(t)][ˉx + x ′(t)]
′ ′
≡ (wˉ+ w )(ˉx + x)
= wˉˉx + w ′ˉx + x′ ˉw + x ′w ′ (2.15 )](aer31x.png)
![[ ( )]
ln -zr-
z0,m](aer36x.png)
![[ ( ) ( ) ( )]
z - D z - D zr - D
ln ------- - ψm ------ + ψm -------
zr - D L L](aer38x.png)
![[ ( ln(z ∕zs ) )] -1
fd = 1.0 - ---------0,m--0,m------ (2.21 )
ln{0.35[(0.1∕zs0,m)0.8]}](aer42x.png)
![{ }
∘Cn---[ ( ) ( )] -2
Cm(z) = Cnm 1 + ----m- ln z- - ψm z- (2.29 )
k zr L](aer45x.png)
