A model for mineral dust emission - Wiley Online Library

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Sep 16, 2001 - A model for mineral dust emission. Yaping Shao. Department of Physics and Materials Science, City University of Hong Kong, Hong Kong.
JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 106, NO. D17, PAGES 20,239-20,254, SEPTEMBER 16, 2001

A model

for mineral

dust

emission

Yaping Shao Departmentof Physicsand MaterialsScience,City Universityof Hong Kong, Hong Kong

Abstract. In the new dust emissionmodelpresentedin this paper, the two major dust emissionmechanismsare considered,namely, saltation bombardment and aggregatesdisintegration. The emissionof dust generatedby the first mechanismis modeledfrom the perspectiveof volume removal causedby saltating particles and that arising from the secondmechanismis related to the streamwisesaltation flux. The dust emissionrate is constrainedby usingthe informationof minimally and fully dispersedparticle size distributions. The performanceof the dust emissionmodel is comparedwith the available field measurements.Despite large uncertainties both in measurementsand model parameters, the comparisonshowsthat the model is promising. The accuracyof the model dependson the availability of high-quality particle size data. It is proposedto establish a detailed database of particle size distributionsfor varioussoil types for the purposeof modelingdust emissionover large areas. 1. Introduction

ing a supplyof saltatinggrains,followedimmediatelyby a dust bed subject to saltation bombardment. On the Mineral dust generatedby wind erosionis believedto basisof the experimentalresults,$hao et al. [1993]debe the most important sourceof atmosphericaerosols. rived a dust emissionmodelfrom the view point of parEstimatesof total global dust emissionrange between ticle bindingenergyand the energybalanceof saltating 1000 and 5000 Mt yr-•, and a widely cited value is particlesduring the particle and surfacecollision.They

3000Mt yr-• [TegenandFung,1994].However,these estimates have large uncertainties. The truth is that very little is known about the global dust emissionrate and even less about

the size distribution

of airborne

dust particles. This situation is unsatisfactorybecause it is known that aerosolsinfluence atmospheric radiations through absorption and scattering and through modifying the optical and physicalpropertiesof clouds. One of the main reasonsfor the lack of understandingof dust sourcesis that we have not yet developedadequate modelsfor the computation of dust emissionrate. Dust emission rate, F, is the vertical mass flux of dust at the surface. There have been attempts to relate

hypothesised that the dustemission rate,P, of particle size da generated by the saltation bombardment of particle size ds can be expressedas

P(da, ds) - a(da,ds) •b(da) '

(1)

where O isthestreamwise saltation fluxofparticle size d,, a is a coefficient (dependingboth on da and d,), ma is the dust particle m•s, g is gravity acceleration,and • is the particlebindingenergy(dependingon da). By

relating•(da) to the thresholdfrictionvelocityu,t(da) for dustparticlesof sizede [ShaoandLeslie,1997],the

F to frictionvelocityu, [e.g.,Nicklingand Gilles,1989; above expressioncan be simplified to 1993]). The empiricalexpressions showthat F ocu,",

P(dd,d,) - •(dd,d,)O(d,)ujf(dd),

(2)

with n varying between 2 and 5. The main deficiency of this type of approach is that it does not adequately where/• is an empiricalfunctionof dd and ds. The detake into considerationof the properties of the aeolian pendencyof/• on da and ds arisesfrom the fact that in surface.

(1), a dependson ds and •p is a functionof dd. Wind $hao et al. [1993]carriedout wind tunnel experi- tunnel observationsseem to support this dependency. ments on the emissionof loosely packed dust particles For instance,Shao et al. [1993]have observedthat causedby the abrasiveimpacts of saltating particles, a

mechanism

referred

to as saltation

bombardment.

In

those experiments,two beds of material were placed in the wind tunnel, i.e., an upstream sand bed for provid-

P(da,d,)/O(d,)isindependent ofwindspeed fora specific saltationparticle size class,but for a given wind speed,it increases with ds and decreases with dd. The empiricalexpression of/• derivedby fitting to the data of $hao et al. [1993]is

Copyright2001 by theAmericanGeophysical Union.

/•(dd,as) = [0.6ln(ds)+ 1.6]exp(-140da),

(3)

Papernumber2001JD900171. 0148-0227/01/2001JB900171

$09.00

where dd and ds are in millimeters. Conceptually,this 20,239

20,240

SHAO: MODEL

FOR MINERAL

model is a significantimprovement, as it takes into account both wind and soil conditions. However, while the model is simple and containssomesoundphysics, it has two intrinsic problems. First, it is difficult to estimate accurately •b on either theoretical or experimental grounds. The uncertainty involved in the theoretical estimatesof •b can be severalordersof magnitude. Second,during the particle-surfacecollision,the kinetic energy of saltating particles is not conservative,as a proportion of it convertsto heat.

Lu and $hao [1999]proposeda dustemissionmodel which estimates

dust emission rate on the basis of vol-

ume removal causedby saltating particles as they impact the surface. In summary, it predicts the dust emissionrate (for all dustparticlesizes)causedby the saltation of particles of size ds as

DUST

EMISSION

wise saltation fluxes. Details of the simulation are give

by Lu and $hao [1999]. In general,the modelsproduceda reasonableagreementwith the measurements. In assessing the performance of the models,it is worthwhile to note that the parametersusedin the models of Lu and$hao[1999]and MarticorenaandBergametti [1995]are derivedmoreor lessfromthe samedata set, whilethoseusedin the modelof $hao et al. [1993]are determined independently. The purposeof this paper is to developa more general model that overcomes some of the deficiencies of the

existingmodels. Again, the basic idea is to relate dust emission to streamwise

saltation

flux but with consider-

ation of two major dust emissionmechanisms,namely, saltation bombardment and aggregatesdisintegration. The information of particle size distributions will be used in the calculation of dust emission. In doing so, the information of particle size distributions becomes an important issuefor the modeling of dust emission.

P(d•) - Cagrlpb 2p (O.24 +C•u,v• (•(ds )' (4)

whereCa and C• are coefficients, r• is dust massfrac- This paper constitutesthree basicparts: (1) a discusresponsible for dustemission,(2) tion, Pband pp are bulk-soiland soilparticledensities, sionof the mechanism a description of the new dust emission model,and (3) respectively,and p is the plastic pressureof the soil surface. To estimate

dust emission rate from soils with

an attempt of comparingthe new model with the data

a particle sizedistributionp(d), particlesare separated of Gillette[1977]. into the categoriesof dust and sand. An integration of (4) over the sand particle sizesgivesthe total dust 2. Mechanisms for Dust Emission emissionrate F induced by the saltation of sand partiThe aerodynamic forcefa, the gravityforcefg, and clesof all sizes,namely, the interparticle cohesiveforcefi, act upon soilparticles on a surface. The balanceof theseforcesdeterFP(d)p(d)Jd, (5) resting minesthe entrainmentof particlesinto the atmosphere. The mechanismsresponsiblefor the entrainment of sand where d• and d2 are the lower and upper limits of sand and dust particles differ profoundly becauseof the relparticle diameters, i.e., d• _• ds _• d2. ative importance of the forcesacting upon them. The

•d d2 1

The strengthof the modelof Lu and Shao[1999]is gravityforceis proportionalto d3, i.e.,

that it has a clear representationof the microphysicsof the dust emissionprocess.However, it also has several limitations, namely, (1) as will becomeclear later in the paper, Ca is the releasedfraction of dust contained in the volume removed by the saltation bombardment. This quantity varieswith the bindingstrengthof the soil and dependson particle sizeamongmany other factors. (2) The quantity p is basicallyan unknownquantity that, like •b, containslarge uncertaintiesand (3) the model is basedonly on volume removalor abrasionand may not be applicable to all situations of dust emission.

Marticorenaand Bergametti[1995]haveproposeda purely empirical dust emissionscheme F

• - 0.01 exp(0.308r/clay - 13.82). (6) Here, Q is the streamwisesaltation flux of all sand par-

7rppd 3 and the aerodynamic forceis proportionalto d•, i.e.,

f, - Kapu2, d2, where p is air density and K, is a dimensionlesscoefficient. The cohesiveforce, consistingof the van der Waals, electrostatic, capillary, and chemical binding forces,is essentiallya stochasticvariable which cannot be describedprecisely but is in principal proportional to d. Consideringthe van der Waals force in an idealized situation, for example, that betweentwo spherical particles in vacuum, a possibleapproximation for fi is hw

ticlesizes, r•clay isclayfraction, andF/Q isinm-•. The aboveexpressionis derivedby fitting F/Q to the data of Gillette[1977]. Figure I showsa comparisonof the three dust emis-

wherehw is a coefficient and rmin is a the smallest seperationallowedbetweenthe two particles. Figure 2

showsfg, fi, and fa asfunctionsd, with the parameter [1977],whichalsoincludedthe measurements of stream- valuespp----2650kg m-s, p - 1.2 kg m-3, Ka = 50,

sion models described

above with

the data of Gillette

SHAO' MODEL FOR MINERAL DUST EMISSION

20,241

.........

ß 10•

Soil 5

Soil 5

10-•

10-3

/

• Observed

ß Observed

10" ß-----

10'•

Simulated

-- - Shao etal.(1993) /

-•10 -7

-'----Lu&Shao •'1999• .......

/ 1010_•

- - Marticorena & Bergametti (1995)

•o• 10-

Soil 4

Soil 4

10-2

/

.• •/-

10-3

]

t::]

10 "•

,/• •

10-4

10 -•

/

.........

lO-7

10-" 10-4

10-

Soil 3

Soil 3

r• 10-•

10-•

10-• •

T• 10-3

œ

CY10'-'

10-?

/ // /

10-•

,

10-

Soil 2

10"" 104

Soil 2

10-2

10-s

10-3

10-•

10-"

10-7

10'-5 10-'

,

lO_•

10-

Soil 1

Soil 1

10-2

10"s

10-3

10-7

10-4

10-"

10-5

10-" 0.1

0.2

-1

1.0

O.

u.(ms )

0.2

-1

1.0

u.(ms )

Figure 1. A comparisonof the modeledstreamwisesaltationfluxesand dust emissionrates

withthefieldmeasurements of Gillette[1977]forfivesoils.Themodeled dustemission ratesare

obtainedusingthree differentdust emissionmodels.

2

-2

andhw/rmi n = 0.02J m . Theaerodynamic force fa of scatterin the measurements of fi occurs for nearly

is estimated for u, = 0.4 m s-•. While all three forces identicalmacroscopic conditions.This scatterincreases

decrease with particlesize,fy and fa decrease faster with decreasing particlesize, and the spreadcan be

thanfi. In thisexample, forparticles withd < 20/•m, aslargeasseveral orders of magnitude. Zimon[1982] fi dominates, and hence,the particlescannotbe lifted hassuggested varioustechniques for measuring coheat thegivenu,. Forparticles with20_> u,t, and a suitable

(15) (16)

pc(d)Jd,

(19)

wherepc(d)is givenbypc(d)- pf(d) - pro(d).In (19),

one is

7 - e-•'("'-"")",

•c -- •f -- •m --

•f is the sumof the free and the aggregateddust,that

(z7)

with k and n being empiricalcoefficientsthat can be de-

terminedby fitting (17) to experimental data [Lu,1999]. In (17), u,t shouldbe understoodas the thresholdfric-

is, the total fraction of dust which can be released from an unit soil mass,

rlf --

pf(d)Jd.

(20)

tion velocity of the surface. In Figure 5, a comparison Equation(20) providesan upperlimit for dustemission of the modeledps(d) using(14) with the experimental that is possiblefrom an unit soil mass. The estimates

data of Alfaro et al. [1997]is shownfor threedifferent of r/mandr/f are practicallyimportant,asthey provide velocities. the upperand lowerlimits of dust emissionfor a given

friction

In correspondencewith the particle size distribution, soil type. it seemsplausibleto suggestthat two levelsof binding 3. The fraction of dust (originatedfrom an unit soil energiesexist, namely, a lower level of binding energy, mass)suspended in the atmosphere, namelythe mineral

SHAO: MODEL

FOR MINERAL

DUST EMISSION

20,245

15 o measured o

o

Modeled

o

lO

o

o

Fully disp.comp. Min. disp.comp.

-l

u, = 0.40 ms

10

1oo

l0

oo

o

-l

u, = 0.45 ms lO0 15

o

lO

o o

-l

u, = 0.53 ms 0

1

lO0

l0

d(pm)

Figure 5. Particle sizedistributionsof airborneparticlesgeneratedby the bombardmentof pure

sandgrainsovera claysurfacefor threefrictionvelocities[Alfaroet al., 1997].The originalparticle sizedistribution of thetargetclayis similarto the measurements (opencircles)at u. - 0.4 m s-1 . The modeledparticlesizedistributionsusingequation(14) (thick solidlines) are comparedwith the observations. The pf(d) component(dashedlines)and the pm(d) component(dot-dashed lines)usedin equation(14) are alsoshown.The parametersusedfor estimating-• are u.t - 0.27 m s-1, n- 3, and k- 27.3.

aerosol,can be estimated from

• -

p•(d)5d.

quantities,namely,the streamwisesaltationflux Q and the number flux of striking particles ns, are of particu(21) lar importance. For the saltation of uniform particles, a variety of expressions existsfor the calculationof Q.

It is sometimes desirable to estimate the fraction of

For example,in the Owen[1964]model,Q is givenby

dust for a givenparticlesizerange. Supposethe particlesare dividedinto I particle sizeintervals,eachwith a

2

•,t

Q-Co•U3,(1 - u-?),

mean value di and an increment Adi. For each particle

sizeinterval,•,•,i, •fi, •i and•ci (corresponding to •,•, •f, •, and•) canbe estimatedfrom

etc.

(23)

where Cois a coefficient.Supposewe have particles of size d and mass m. Also supposethat these particles strike the surfacewith velocity U1 and angle al and lift off with velocity U2 and angle a2. The momentum balance of the saltation layer requires that

d+Adi/2 •rni --Jd-Adi12 pm(d)6d, (22)

pu•,(1 - u,t

4. Theory of Saltation

n8- m(U• cos a•- U•cos a•)'

(24)

The saltationof sandsizedparticlesplaysa criti- From (23) and (24), we find the relationship between cal role in the processof dust emission.Two saltation n• and Q, i.e.,

20,246

SHAO:

MODEL

Qg

m½o U,(U1coso•1 - U2cos0•2)' 5. Dust

Emission

FOR MINERAL

EMISSION

particledoesnot rotateduringthe ploughing pro(25) ing cess.As the particlemovesthroughthe soil,it experi-

Model

In calculatingthe total dust emissionrate, we distinguishthe dust emissionin the absenceof saltationfrom that in the presenceof saltation, namely,

encesa resistancethat is proportionalto the particleto-soilcontactareaandto the particlevelocitysquared. It also experiencesan elastic force in the vertical direction, which is soil dependent. The removedvolume is

calculatedas the productof the areasweptout by the particleand the width b • d of the ploughingface,

F-l Fa weak wind, no saltation . (26) Fb + Fc strong wind, with saltation

DUST

•-b

dt dr, t.YrdXr

(27)

As arguedpreviously,Fa arisingdirectly from aerodynamic entrainment is small, and one may follow Loos- with tc being the time at which ploughingceases.It was

moreand Hunt [2000]for its calculation.Here we are assumedby Lu and Shao[1999]that the forceexperi-

encedby the particle during ploughingis a constant, p, consideredto be the plastic pressureof the soil exerted upon the particle. This constant was then treated as a 5.1. Dust Emission From Saltation measurableproperty. While the constantp assumption Bombardment: Fb allowsanalytical solutionsfor the volume removal,it is The dust emission rate Fb, arising from saltation physically irrational becausethe resistancethe particle bombardment can be modeled on the basis of the volexperiencesmust be proportional to its velocity. In adumes removedby sand grains as they impact the soil dition, p is not a soleproperty of the soil but a variable surface. The scheme used here for the calculation of that dependson the properties of both the soil and the the removal is based on similar ideas of Lu and Shao particle, for example, impact particle size and speed. [1999]but with modifications.The process of volume The equations of particle motion in the X and Y removalby saltationbombardmentis illustratedin Fig- directions used in this paper are ure 6 which showsthat as a saltating particle strikes the surface,it createsa crater and ejectsparticles into dup the air. The saltating particle is assumedto be spherim•-•-+axpx- 0 (28)

mainly concernedwith the latter case.

calwith diameterd andmassm - •17•A gpd3. The origin dvp of the coordinatesystemis located at the centroidof m•+aypy - 0 (29) dX the saltating particle when it starts to contactthe surface. When consideringthe saltation bombardment,it dt Up - 0 (30) is assumedthat the particle doesnot break during the dY impact. The particle strikes the surface at a velocity dt Vp - O, (31) U1 and an angle al. It then ploughesinto the surface and coversa trajectory (X•,, YT) in the target soil and whereax anday arethe particle-to-soil contactareasin forms a crater. the X and ¾ directions,respectively.Thesetwo areas For simplification, we further assumethat the saltat- can be approximated as follows

Figure 6. An illustrationof volumeremovalprocessby saltationbombardment. A saltating particle ploughesthroughthe soil, createsa small crater, and ejectsparticlesinto the air.

SHAO: MODEL

FOR MINERAL

DUST

EMISSION

20,247

the massflux of saltating particlesstrikingthe surfaceis runs. The massfraction of soil aggregatesavailablefor breakingis r/c given by (19). Hencethe dust emission arisingfrom aggregates disintegrationcan be expressed

_ _ {ød•' -b Y-