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AD-A237 024
Defense Nuclear Agency IAlexandria, VA 22310-3398
DNA-TR-90-71
Target Area Operatirng ConditionsDust Lofting from Natural
Surfaces
R. A. GajR. D. SmallPacific-Sierra Research Corporation12340
Santa Monica BoulevardLos Angeles, CA 90025-2587
OTICJune 1991 ELECTE
Technical Report
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Lofting from Natural Surfaces PE - 62715H
6. AUTHOR(S) PR - RATA - RG
R. A. Gaj, R. D. Small WU - DH044920
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13 ABSTRACT (Maximum 200 words)
We explore how variations in soil type, vegetation cover, and
climatic conditions influence thesweepup mass in target regions. A
simple dust sweepup/suspension model, appropriate forthe high wind
speeds associated with nuclear blast waves, is developed to depend
explicitlyon the threshold shear velocity required to initiate dust
lofting. Given an analytic driver forthe positive phase free stream
wind speed versus ground range and time, sweepup massesfor a wide
range of surface types and conditions are calculated. We find that
for an airburstat SHOB = 500 ft/KTI / 3, the sweepup mass can be
reduced to near zero If the surface is cov-ered with tall grass or
a mature small grain crop. For bursts over loose, unvegetated
sand,sweepup efficiencies are nearly six times greater than for a
typical Nevada Test Site surface.For a lower altitude alrburst
(SHOB = 50 ft/KTI /3), a somewhat smaller variation betweenthese
extremes is predicted (e.g., scouring is possible even over grass
or cropland). The yielddependence of sweepup mass and the surface
area scoured by the blast winds is also ex-plored. The results
indicate that the net dust injection from a nuclear laydown can
vary sig-nificantly within individual target areas and may be a
strong function of season-especiallyin agricultural regions.
14 SUB.'ECT TERMS 15. NUMBER OF PAGESSweepup Soil Target Areas
38Scouring Threshold Velocity Vegetation 16. PRICE CODEDust Lofting
Boundary Layers
17 SECURITY CLASSIFICATION 18 SECURITY CLASSIFICATION 19,
SECURITY CLASSIFICATION 20. LIMITATION OF ABSTRACTOF REPORT OF THIS
PAGE OF ABSTRACT
UNCLASSIFIED UNCLASSIFIED UNCLASSIFIED SAR
NSN 7540-280-550) Standard Form 298 (Rev 2-89)Piescibed by ANSI
Slt 239.18298 102
-
UNCLASSIFIEDSECURITY CLASSIFICATION OF THIS PAGE
CLASSIFIED BY:
N/A since UnclassifiedDECLASSIFY ON;
N/A since Unclassified
SECURITY CLASSIFICATION OF THIS PAGE
UNCLASSIFIED
-
PREFACE
Fratricide probabilities are derived from model predictions of
nuclear clouds. Exper-imental data are sparse and alternative
validations are needed. Pacific-Sierra ResearchCorporation (PSR)
has examined several key issues where uncertainties are large
andrecommended validations for three such areas. They include: the
influence of surfaceconditions on the sweepup mass of nuclear
clouds; fireball quenching by entrainedmass; and long range cloud
transport.
In Vol. 1 of this report series, smoke plumes and obscurations
above target areas wereconsidered. Volume 2 considered long range
dust transport and Saharan dust eventsas an analog for dispersion
of nuclear clouds. Volume 3 recommends high energy ex-periments to
simulate fireball-particle interactions.
In this volume, we develop an analysis for the mass entrained by
nuclear clouds. Realsoil moisture and vegetation cover are
accounted for and it is demonstrated thatsweepup mass in some
target areas is considerably less than currently estimated.
This research was performed under contract DNA 001-87-C-0298 and
monitored byDr. Charles R. Gallaway, Shock Physics Weapon Effects,
Defense Nuclear Agency.
NT~Ij GRA&I
DTIC TABUnannounced E3j u s i i c a t i o n ---
- - -
ByDistributioc/ de-AvailabilitY Codes.
ii
-
CONVERSION TABLE
Conversion factors for U.S. customary to metric (SI) units of
measurement
To Convert From To Multiply
angstrom meters (m 1.000 000 X E-10
atmosphere (normal) kilo pascal (kPal 1.013 25 X E+2
bar kilo pascal (kPal 1.000 000 X E+2
barn meter 2 (m 2 ) 1.000 000 X E-28
British Thermal unit (thermochemical) joule (J 1.054 350 X
E+3
calorie (thermochemical) joule (J) 4.184 000
cal (thermochemical)/cm 2 mega Joule/m 2(Mj/m 2) 4.184 000 X
E-2
curie giga becquerel (GBq)* 3.700 000 X E+ I
degree (angle) radian (rad) 1.745 329 X E-2
degree Fahrenheit degree kelvin (K) tK=(tof + 459.67)/1.8
electron volt Joule (J 1.602 19 X E-19erg joule (J 1.000 000 X
E-7
erg/second watt (WI 1.000 000 X E-7
foot meter (ml 3.048 000 X E-l
foot-pound-force joule (J) 1.355 818
gallon (U.S. liquid) meter (m3) 3.785 412 X E-3inch meter (m
2.540 000 X E-2
jerk joule (J) 1.000 000 X E+9
joule/kilogram (J/Kg) (radiation doseabsorbed) Gray (Gy) 1.000
000
kilotons terajoules 4.183
kip (1000 lbf) newton (N) 4 448 222 X E43
kip/Inch 2 (ksil) kilo pascal (kPa) 6.894 757 X E+3
ktap newton-second/m 2 (N-s/m 2) 1.000 000 X E+2
micron meter (ml 1.000 000 X E-6
mil meter (ml 2.540 000 X E-5
mile (international) meter (ml 1.609 344 X E+3
ounce kilogram (kg) 2.834 952 X E-2
pound-force (lbf avoirdupois) newton (N) 4.448 222
pound-force inch newton-meter (N-m) 1. 129 848 X
E-Ipound-force/Inch newton/meter (N/rm) 1.751 268 X E+2
pound-force/foot 2 kilo pascal (kPa) 4.788 026 X E-2
pound-force/inch 2 (psi) kilo pascal (kPa) 6.894 757
pound-mass (Ibm avofidupois) kilogram (kg) 4.535 924 X
E-Ipound-mass-foot 2 (moment of inertia) kilogram-meter 2 (kg m 2)
4.214 'I I X E-2
pound-mass/foot 3 kilogram/meter 3 (kg/m 3 ) 1.601 846 X E+
l
rad (radiation dose absorbed) Gray (Gy)° 1.000 000 X E-2
roentgen coulomb/kilogram (C/kg) 2.579 760 X E-4
shake second (s) 1.000 000 X E-8
slug kilogram (kg) 1.459 390 X E+ I
torr (mm Hg. OC) kilo pascal (kPa) 1,333 22 X E-I
'The becquetel (Bq) is the SI unit of radioactivity; Bp = I
event/s."The Gray (Gy) is the Si unit of absorbed radiation.
iv
-
TABLE OF CONTENTS
Section Page
PREFACE .......................................................
iii
CONVERSION TABLE ...........................................
iv
FIG U RES
....................................................... vi
I INTRODUCTION ................................................
I
2 CLASSIFICATION OF SURFACE TYPES ..........................
2
2.1 THRESHOLD SHEAR VELOCITY ............................. 2
2.2 OBSERVED VARIATIONS ....................................
3
2.3 SEASONAL VARIATIONS ....................................
4
2.4 NUCLEAR INFLUENCES ....................................
6
3 SW EEPUP MODEL ..............................................
8
3.1 BACKGROUND ..............................................
8
3.2 HIGH SPEED MASS FLUX MODEL .......................... 8
4 SWEEPUP CALCULATIONS .....................................
11
4.1 METHODOLOGY ............................................
11
4.2 VARIATIONS IN SWEEPUP MASS .......................... 11
4.3 VARIATIONS IN SWEEPUP RADIUS . ...................... 13
4.4 NEVADA TEST SITE SOIL ..................... .............
17
4.5 NORMALIZED SWEEPUP MASS ............................. 21
5 IMPLICATIONS FOR TARGET AREAS ...............................
23
6 CO NCLUSIONS
.................................................... 25
7 LIST OF REFERENCES .........................................
26
v
-
FIGURES
Figure Page
1 Threshold shear velocity as function of season for U.S.
agriculturalarea- loam soil
..................................................... 5
2 Threshold shear velocity as function of season for U.S.
agricultural
area- sandy soil
..................................................... 7
3 Blowing parameter as function of normalized shear stress
............ 10
4 Net sweepup mass as function of threshold shear velocity
............ 12
5 Net sweepup mass as function of burst altitude
........................ 14
6 Net sweepup mass as function of yield
............................... 15
7 Effective sweepup radius as function of threshold shear
velocity ...... 16
8 Effective sweepup radius as function of burst altitude
................ 18
9 Effective sweepup radius as function of yield
........................ 19
10 Sweepup mass relative to airburst over Yucca Valley as
functionof threshold shear velocity
.......................................... 22
11 Soils in the Minot AFB, North Dakota ICBM silo area
................. 24
vi
-
SECTION 1
INTRODUCTION
The amount of dust and debris which sured threshold shear
velocities, and (2)can be scoured and lofted into a nuclear a
theoretical mass flux model appropri-cloud depends strongly upon
surface ate for the high surface wind speeds as-conditions in the
target area. Regional sociated with nuclear blast waves. Theseand
seasonal variations in land use, two components are combined such
thatvegetative cover, soil moisture, and soil the vertical dust
flux has an explicit de-texture all influence the sweepup mass
pendence upon the threshold shear ve-source and lead to wide
differences in locity. Time- and range-dependentthe mass injection.
The dependencies nuclear blast winds are prescribed usingare poorly
understood and are not at analytic positive phase dynamic
pres-present accounted for in any DNA sure formulae. Although our
model issweepup model. As a result, broad un- highly idealized (it
cannot, for example,certainties are introduced any time account for
precursor flows or unevensweepup models are applied to target
terrain), the results nevertheless demon-areas outside the region
for which they strate the seriousness of ignoring region-were
originally developed (namely, dry, al and seasonal variations in
target areasandy deserts). This is a serious prob- conditions.
Moreover, they indicate alem, especially considering the geograph-
clear direction for more detailed theoreti-ic variety of strategic
targets areas found cal and experimental work.in the Soviet Union
(e.g., subarctic taigaforests, black soil farmland, wooded
rivervalleys, and semiarid steppes). Sweepup The report is divided
into six sections. Infrom those regions can hardly be ex- Sec. 2,
we describe the surface classifi-pected to resemble sweepup from a
des- cation scheme and discuss how thresh-ert; but currently, it is
impossible to old velocities can vary with soil type anddistinguish
the differences. season., Next, in Sec. 3, we describe the
sweepup model., This model is thenIn this report, we calculate
swecpup applied in Sec. 4 to calculate the totalmasses (without
accounting for material sweepup mass and the "effective
scour-fallback to the surface) for a wide range ing radius" for
various surfaces, heightsof surface conditions. Our approach has of
burst, and yields. The implications oftwo main components: (1) A
surface these results are discussed in Sec. 5,classification scheme
based on mea- and conclusions presented in Sec. 6.
-
SECTION 2
CLASSIFICATION OF SURFACE TYPES
The blast winds generated by low alti- regulated airflow [e.g.,
Gillette, 1978. Astude nuclear detonations are strong the wind
speed in the tunnel is in-enough to scour material from virtually
creased from zero, the shear velocityany natural surface. Dirt,
pebbles, bush-es-even rocks and trees-can be carried r IP/2 dUaway
when subjected to winds in excess -. /P )of several hundred meters
per second. dnZ
Yet, while it is clear some sweep up will is monitored until
saltation (indicated byprobably always occur (especially at
particles rolling or bouncing along theground ranges where dynamic
pressui es surface) begins.' Here r. is the shear
maximize), it is equally clear that theamount of material swept
up is not the stress, p is the air density, k -- 0.4 is thevon
Karmann coefficient, and U Is the
same for all surfaces. Vegetated land, for horizontal wind speed
at some height Zexample, yields less sweepup mass thanbarren
ground; and moist (or frozen) soil above the ground. The value of
U, atless than dry. The key issue is the ability which saltation
first occurs defines theof a surface to resist the shear stresses
threshold shear velocity U,.exerted by a nuclear blast wave and
itsaccompanying winds. Any factor whicheither (a) lessens the
stress applied di- The threshold shear velocity Uth canrectly to
the soil (such as a plant cover), also be used to define the point
at whichor (b) increases the cohesiveness of par- dust enters Into
suspension. This regime,ticulates lying on the surface (such as a
defined by the condition (Owen, 1964high moisture content) tends to
lessenthe susceptibility of the soil to sweepup U,and thus reduce
the net mass lofted. An . (2)explicit quantification of all those
factors Uhas not been developed; however, the begins when the
turbulent drag forcethreshold shear velocity can at least upn I n
prt iles rst exceroughly categorize their net effect for a upon
individual particles first exceedsgiven surface, their
gravitational fall speed. It is at thispoint that the particles
become lofted2.1 THRESHOLD SHEAR VELOCITY. and can be carried to
high altitude. Sus-
pension Is the mechanism which createsThe threshold shear
velocity is a mea- sand and dust storms in arid regions. Itsure of
the minimum shear stress re- is also responsible for the dense
sweep-quired to initiate particle motion along up layers generated
by nuclear air-the ground. It is experimentally deter- bursts.
Equation (2) therefore forms amined in the field using a portable,
op- base for the sweepup model described inen-bottomed wind tunnel
with a Sec. 3.
I. The relation between shear stress and vertical wind shear
given by Eq. (1) is strictly valid only whenthe atmospheric surface
layer Is statically neutral (well mixed). Corrections to this
formula for otherstability profiles are available isee Businger,
19731.
2
-
2.2 OBSERVED VARIATIONS. example, tend to increase U~th in
clay
The concept of using U. as an index for soils by strengthening
their crustal
strength [Gillette, 19821.sweepup potential was originally
devel-oped for application to "normal" (non- All of the soils
listed in Table I were dry.nuclear) conditions such as dust erosion
Technically, this means that the water
from drought-stricken agricultural land content in the first few
inches below the
and deserts. Thus the only systematic surface was at or below
the wilting pointmeasurements made to date have been for most
crops. (The wilting point corre-
over dry, barren, or sparsely vegetated sponds to a water to
soil volume ratio ofground, since such surfaces are most 0.05 for
sandy loams, 0.08 for loam, andlikely to be subject to significant
low- 0.17 for clay [Alderfer, 19771.) It has
wind speed sweepup. Nevertheless, even been found, however, that
once the wa-
for this restricted range of surface types, ter content of a
soil begins to exceed the
wide variations in U h have been found. wilting point (due to
rainfall or irriga-tion), U th increases substantially aboveTable 1
summarizes some of these
varia-
tions. In general, soils which are loose the values listed in
Table 1, although it(e.g., plowed or otherwise disturbed) or is not
clear how much (Chepil, 1956.sandy are the most easily eroded (and
Saturated or frozen soils are likely to be
thus have the lowest Uth ); loamy soils, even more stable, but,
again, no mea-surements are available.
soils with a large number f large ele-ments such as pebbles and
those with a Precipitation can modify the thresholdcrusted or
cloddy surface are the least velocity in other, although less
obvious,erodibie. In most cases, mineral content ways. Sandy soils
which are initially dryalso influences soil erosion potential. and
cloddy, for example, often becomeHigh concentrations of
exchangeable so- more erodable several days to weeks af-dium or
calcium carbonate (CaCO3), for ter a heavy rainfall. This is due to
the
Table 1. Mean threshold velocities for unvegetated soils.
Threshold Percent MassShear Velocity in Particles
fm/s) >1 mm diameter Modulus ofCrustal Rupture
Soil Type Loose Cloddy Crusted Loose Cloddy (bars)
Sand 0.28 0.75 0.66 3 60 0.03Sandy loam 0.29 1.05 2.90 30 64
0.42Loamy sand 0.34 0.85 1.03 26 47 0.5Clay 0.54 >1.50 >2.00
42 94 0.75Silty Clay 0.56 ---- ---- 6 ..Silty clay 0.64 .... >
1.50 18 ..
loamClay loam 0.68 >1.09 1.20 28 81 0.38Loam 0.78 >1.50
>1.50 49 89 0.66Silt loam 1.08 >2.00 > 1.50 77 89
0.8Source: Gillette [1988.
3
-
tendency for rainfall to "melt" (disaggre- upper bound on U.
above which sweepupgate) the clods lying on the surface. commences.
This critical value likely de-Once the soil dries, it returns to a
pends not only on the type of plant andsmooth, loose, and thus more
easily ps stand density (plants per unit surfaceeroded state. On
the other hand, if the rea), but also on the plant height, Itssoil
is Initially loos, wetting and drying ter content, stem thickness,
and aero-may ultimately lead to the formation of a dynamic cross
section. However, for verycrust, thereby increasing U. Timing is
dense plant covers such as small grains
an important issue here: If the surface is or grasses, we expect
that the plantssubjected to strong winds very soon after would
either be lodged (i.e., knockeda rainfall (or snowmelt),
significant dry- over), broken, or uprooted long beforeing of the
upper few millimeters may oc- this critical shear stress is
reached. Thecur before the crust can form. Sweepup surface would no
longer be as well pro-can then follow, even though the soil a
tected and the critical shear velocitycentimeter or two below the
surface is would drop to a value more representa-still
water-soaked. This effect has been tive of bare soils. (Similar
modificationobserved many times in loam and clay would result if
the plant cover wereloam soils [Gillette, 19881. In a nuclear
burned due to pre-shock thermal irradi-environment, thermal
irradiation of the ation.) Unfortunately, no experimentalsurface
may also dry the upper soil hori- data exists which relates high
speedzon, possibly negating the stabilizing in- sweepup to shear
streso over vegetatedfluencc of soil moisture. (This influence
ground, although some measurements ofcould however be mitigated by
a smoke, the critical bending moment for wheatdust, or steam layer
just above the sur- and barley stem breakage have beenface which
would tend to shield the made [Oda, Suzuki, and Odagawa,ground.)
19661. Lacking such data, we arbitrarily
assume that a dense plant cover resultsVery few measurements
have been made in a threshold shear velocity of at least 3of the
effects of live vegetation upon m/s. Clearly, experiments must be
per-sweepup. It has been found, howeve:, formed to refine this
value.that any sort of grass or small grain cropcover (e.g., wheat,
barley, rye) is usually 2.3 SEASONAL VARIATIONS.sufficient to
preclude sweepup for all butthe strongest natural winds All of the
effects discussed above-the(U. ; 2 m/s) influence of vegetation
cover, soil mois-
,Gillette, 19881.2 Even a ture, land use, and soil
texture-imply
sparse vegetation cover with a fractional that the poteatial for
sweepup (andlateral cover (frontal silhouette area di- thus U.,h )
must vary seasonally. Figurevided by ground area) greater about 2
to 1, derived from a database used to pre-4 percent can reduce the
shear stress dict soil erosion in U.S. agriculturalupon the surface
to near zero under nat- areas [Gillette and Passi, 19881,
illus-ural wind conditions [Marshall, 19711. trates the expected
variation U forNevertheless, there presumably exists an th
2. One exception occurs when a planted field lies immediately
downwind from a barren, sandy (lowU.,,) surface from which sweepup
Is occurring. Material from the upwind source can then spreadInto
the field, effectively "sandblasting" the plants and the underlying
ground surface, thus initiat-ing sweepup from where it would
otherwise not be expected [Gillette, 19881. Obviously, such
down-wind sandblasting effect could also be impo.-tant in target
areas containing a mixture of vegetatedand bare (e.g.. fallow)
surfaces.
4
-
6- Loam soil,
spring-planted wheat/barley
5-
-
/Moist year,3- moist previous2- Dry year,
2 / dry previous
i IilI m~llJ I I I qiiil01r
J F M A M J J A S O N D J
Month
6
Loam soil, fallow5
4
EMoist year,3- 3moist previous
0 Dry year,~dry previous,-~ ~ / ,._,...i
J F M A M J J A S O N D J
Month
Figure 1. Threshold shear velocity as function of season for
U.S. agricultural area-loam soil.
5
-
loam soil as function of time of year for have a crucial
influence upon sweepup.two land use types (fallow land and a For
example, thermal radiation incidentspring-planted crop) and for two
"clima- upon the surface prior to arrival of thetic" classes
(corresponding to a pro- blast wave can heat the soil to a
pointlonged moist period and a prolonged where bound water is
explosively re-drought, respectively). A similar plot for leased,
thus causing "popcornlng" ofsandy soil is shown in Fig. 2.
Obviously, particles from the surface [Versteegen,the most
important influence is the pres- Rault, and Hillendahl, 1989]. This
effect,ence and maturity of the crop (in this which is most
prevalent for clay soils,case, assumed to be a small grain cere-
may disrupt surface crusts and loweral), which greatly Increases
the 3,tability the threshold velocity of the soil. On theof the
soil from shortly after germination other hand, thermal irradiation
can alsoin the spring until harvest in late sum- melt or "glaze"
the surface, thereby sta-mer. On the other hand, in spring, when
bilizing the soil by leaving a thin butthe ground is plowed, crusts
and clods presumably strong crust. Sandy sur-are broken, the
threshold velocity is re- faces are probably the most
susceptibleduced, and the soil becomes more vul- to glazing,
although it has only rarelynerable to wind erosion. After harvest,
been observed, most notably followingthreshold velocities remain
moderately the TRINITY test in 1945 [P. Verstecgen,high due to the
common practice of leav- personal communication, 19891.ing a
vegetative residue or stubblethrough the winter. In drought years,
Blast effects can also modify the dusthowever, insufficient
moisture is avail- producing potential of the surface. Air-able to
support this residue and clodding blast loading of subsurface air
pores canand crusting of the surface is inhibited, cause spalling
and disruption of an un-Threshold velocities therefore remain
broken surface with the passage of thelow. blast wave. The blast
can also uproot
trees and bushes, which would break2.4 NUCLEAR INFLUENCES. the
surface and reduce the threshold ve-
locity, as well as increasing the shearThreshold velocity
measurements to date stress upon the ground. Models relatinghave
focused only on conditions likely to blast effects to tree blowdown
do existbe encountered under normal condi- [Morris, 19731; however,
no quantifica-tions. In a nuclear environment, howev- tion of its
effect upon soil lofting is yeter, several other factors may prove
to available.
6
-
6Sandy soil,Spring plantedwheat/barley - -
4 /
_E - Moist year,moist previous
Dry year,dry previous
0/
J F M A M J J A S O N D J
Month
6-
Sandy soil, fallow5-
4
E Moist year,,3 - moist previous
2- rydry previous
J F M A M j J A S O N D J
Month
Figure 2. Threshold shear velocity as lunction of season for
U.S. agricultural area-sandy soil.
7
-
SECTION 3
SWEEPUP MODEL
In the previous section, we reviewed very few measurements of F
in this re-many of the links between surface condi- gime,
especially at the very high windtions and the potential for dust
lofting. A speeds characteristic of nuclear blastgeneral model
would account for soil waves. In one experiment [Hartenbaum,type,
texture, moisture, temperature and 19711, a value P = 1.0 was found
overvegetation. In this first analysis we an uncohesive sand (mean
particle ra-roughly account for all parameters usinga single
quantitative measure-the dius 1251im; U~th 0.35 m/s )
surfacethreshold shear velocity. The sweepup for free stream wind
speeds U betweenmodel we develop is clearly an approxl- 34 and 115
m/s (corresponding to shearmat ion, but nonetheless accounts for
velocities in the range 5.0 __ U. -5 18.6real soils In calculating
the amount ofdust leaving the surface., m/s). This result cannot be
easily ex-
plained by simple dimensional analyses.3.1 BACKGROUND. A model
which accounts for the effect of
dust loading on the airstream at verySweepup models relate the
vertical mass high wind speeds is required.flux F of dust particles
leaving the sur- 3.2 HIGH SPEED MASS FLUX MODEL.face to the shear
stress T. = p U. 2 ex-
erted on the ground by a sheared For wind speeds In the
regime(rotational) wind field. The general form U, ;> 10 U.th
Ithe vertical mass flux isis related to the surface shear stress
by
(Mirels, 1984):F = a ( U, - U .1h ) ( 3 )F
2 t n(1 +B)(4
where U, > U.t h and a and P3 are empir- Uo
ical coefficients. At low wind speeds, di- where Po and U0 are
the density andmenslonal analysis suggests that F horizontal wind
velocity In the freeshould vary with the kinetic energy de- stream
(i.e., at the top of the dusty sur-livered to the surface
[Gillette, 19801. face layer) and B is a dimensionlessThus we
expect /3 = 3; this dependence blowing parameter which expresses
the
effect of transverse particle injection onhas indeed been borne
out by observa- the local shear stress In plane paralleltions of
natural sweepup from desert flow. Assuming that the mass loading
ef-surfaces [Shinn et al., 1976; Westphal, fectively reduces the
shear stress to theToon, and Carlson, 19871. However, as threshold
value required to maintainwind speeds rise arid dust concentra-
dust lofting, B is given by the implicit re-tions increase, the
lofted particles begin lationto act as a momentum sink on the
air-flow. Thus the shear on the surface is 2reduced, the lofting
ability of the wind Un(l + B) = B (5)diminished, and F is no longer
propor-
tional to U. 3. Unfortunately, there are
8
-
which, In the suspension regime the "rough plate" formula
[Schlichting,(U. > 10 U.th), can be approximated 19581:
U, = - [2.87 + 1.58 log(x/Ks)]-1 .25
kn(1 + B) = 3.92 (6) (7)U.th
where x is the distance behind the shockwave, K. . 0.05 m is the
roughnessheight, and x > 100 Ks. Finally, substi-
The functional dependence of B on the tuting Eqs. (6) and (7)
Into Eq. (4), we ob-shear stress ratior./r.th given by Eqs. (5)
tain [see Eq. (8) below]
and (6) is illustrated in Fig. 3. The sweepup mass flux is
therefore in-versely (but weakly) dependent upon
To prescribe U0 as a function of time, threshold velocity. This
expression com-
groud prngeibel, and hfn ti of bu, pares well with the
experimental result Fground range, yield, and height of burst, c
Uo1 .' 44 derived by Hartenbaum [ 1971J]
we use the ideal airblast approximations deuetly u atebasi
for
given by Brode (1987). These approxima- and subsequently used as
the basis for
tions are valid only during the positive many nuclear sweepup
models
overpressure phase of the blast; we [Schlamp, Schuckman, and
Rosenblatt,
therefore assume all the sweepup occurs 1982; Bacon, Dunn and
Sarma 1988.
during the positive phase. The free- However, unlike previous
models, the de-
stream velocities are then used to com- pendence of sweepup on
threshold veloc-ity (and hence on surface type) is explicit
pute the shear velocity U, according to in Eq. (8).
1.80 po 1.240.24 [2.87 + 1.58 log(x/Ks)] 2.80U *th
9
-
10~6
10 Q5
10 _~
E 0Analytic~ /
r- 102 /0
101 /
100
1O0 II100 101 102 1014 0
Normalized shear stress, U.2/Uth 2
Figure 3. Blowing parameter as function of normalized shear
stress.
10
-
SECTION 4
SWEEPUP CALCULATIONS
We now use the mass flux model and no sweepup occurs (AMMAX =
0). Thusideal blast wave driver to compute the RMAx-i = RE defines
the effective sweep-variation in net sweepup as a function of up
radius. The total sweepup mass M isthreshold shear velocity. Two
quantities then found by simply summing over theare of interest:
(1) The integrated sweep- rings:up mass M; and (2) the effective
sweepupradius RE, defined as the the maximum IMAXrange (from ground
zero) at which M = AM . (10)sweepup can occur for a given yield,
i=lHOB, and surface type.
Note that M is a measure of the initial4.1 METHODOLOGY. sweepup;
it does not account for mass
fallback to the surface, nor does it in-We treat the surface as
fiat, homoge- elude mass lofted during the negative
neous (i.e., no spatial variations in phase.
threshold velocity), and thermally ideal.
Assuming cylindrical symmetry about 4.2 VARIATIONS IN SWEEPUP
MASS.the burst point, the incremental dustmass AMi lofted from a
ring of width AR We have computed the variation in totaland radius
Ri is sweepup mass M for threshold shear ve-
locities from 0.20 to 4.0 m/s, scaledIT + D heights of burst
(SHOBs) from 20 toAMi = 2,T RiAR Fidt (9) 1000 ft/KT" /3 , and
yields (W) from 500
to 1000 KT. 3 Figure 4 shows the depen-dence of M on U~t for a
500 KT detona-
where T is the blast wave time of arrival dth
at Ri, Du is the dynamic pressure posi- tion at three burst
altitudes: 397 fttive phase duration, and F, is the local (SHOB =
50 ft/KTI 3), 1984 ft (SHOB =sweepup mass flux (Eq. 8). We set ARi,
250 ft/KT"/3), and 3969 ft (SHOB = 50060 m and use empirical
formulae to de- ft/KT"13). We find that M decays expo-termine T and
D,, as functions of height nentially with increasing U*,h , and
isof burst, yield, and range [Brode, 1987). most sensitive to
variations in thresholdTo simulate the low windspeed cutoff for
velocity at low U.ih -i.e., over dry, loose,dust suspension, we
further assume F, =0 for U, < 1U h. unvcgetated soils. In this
regime, small
changes in surface type can produce
Equation (9) is integrated numerically large changes in sweepup.
For example,
using the trapezoidal rule and a timestep we find that a 50 ft
SHOB detonation
At = D/100 for= 1 toi= IMAX where over loose sand (U*,h = 0.28
m/s) raises
IMAX corresponds to the first ring where over two times as much
mass as an
3. The burst altitude SHOB = 20 ft/KT"' 3 roughly corresponds to
the minimum for non-cratering air-bursts [Rosenblatt, 19811.
II
-
cImCL
M E
-44
Co 0 0C) (n/0
U(I
LO -~ L
II
I::I!~ 3n) 000Q)4
l>.Cu *
0.5
-oo
000 ~00
(1)V 'ssew dndeemS
12
-
identical burst over loose loam (U. = tive to the results in
Fig. 5 for allSHOB h 650 ft/KT1 3.0.78 m/s). If the burst occurs
at
an even
higher altitude (e.g., 500 ft SHOB), the Sweepup also increases
with yield. Fig-difference is more pronounced. For high- ure 6
shows the variation in M for fourly non-erodible soils (Uth >
2.0) or soils surface types and two burst altitudes (50
which are densely vegetated and 250 ft SHOB) for yields between
500KT and 1 MT. The calculations show a(U 3linear dependence on
yield in this range,
pressed, especially at higher burst alti- with sandy surfaces
being the most sen-tudes. Indeed, we find that when a 500 ft sitive
to changes In W and desert pave-SHOB detonation occurs over a
surface ment the least. Thus the sweepupwith U.th > 3.5 m/s
(characteristic of an efficiency (defined as soil mass lofted
perearly to mid-summer wheat crop-see megaton of weapon yield) is
yield depen-Figs. t and 2), no sweepup occurs at all. dent. For
example, a 500 KT burst at 50
ft SHOB produces sweepup efficiencies
ranging from 0.12 Tg/MT for desert
The strong dependence of sweepup mass pavement to 0.33 Tg/MT for
sand. Rals-
on burst altitude Is Illustrated in Fig. 5. Ing the yield to I
MT, however, nearly
Here we have plotted M as a function of doubles these values to
between 0.23
SHOB for a 500 KT burst over four sur- and 0.64 Tg/MT. Slightly
lower efficien-
face types ranging from loose sand to a cies result at all
yields when the burst
desert pebble pavement (mass equivalent occurs at a higher
altitude (250 ft SHOB)modal pebble diameter 1.0 cm) similar to over
the two least erodible surfaces
that found in Yucca Valley at the Nevada (loam and desert
pavement), while higher
Test Site (NTS)., We find that the depen- efficiencies are
obtained over the most
dence of M on SHOB is highly nonlinear, erodible ones. This is
consistent with
with the largest variations occurring over Fig. 5.
the most erodible soils. In particular, we 4.3 VARIATIONS IN
SWEEPUPfind that sweepup mass at first decays RADIUSrapidly with
increasing SHOB, reaching RADIUS.a relative minimum around 80 to
100 ft The variations in sweepup mass dis-SHOB. With further
increases in burst cussed above can be attributed to a
com-altitude, however, the sweepup mass be- bination of two
factors: (1) Variations ingins to rise-indicative of the build-up
in positive-phase dynamic impulse inte-blast dynamic pressure with
Increasing grated over the sweepup area, and (2)SHOB for shocks
waves in the Mach re- variations in the size of the sweepupflection
regime. The positive dependence area itself. Sweepup area can be
charac-of M on SHOB continues until an alti- terized by the
effective sweepup radiustude is reached at which the Mach wave RE.
Figure 7 shows the dependence of REbegins to weaken-typically
between 300 on threshold shear velocity for threeand 400 ft SHOB.
For bursts above this burst altitudes. Comparing these
resultsaltitude, sweepup again diminishes, with Fig. 4, it is clear
that the sweepupeventually dropping to zero. Over desert mass M
depends strongly upon RE-bothpavement, the cutoff occurs at SHOB
=760 ft/KT"' 3 (HOB = 6032 ft); over loam, decay exponentially with
increasing U,th'it is at SHOB = 935 ft/KT 1 3 (HOB = and both
display the greatest sensitivity7421 ft). These results are
modified to threshold velocity over bare, loose soil.somewhat over
non-ideal surfaces due to (Not all the dust to radius RE is lofted
toenhanced velocities in the precursed stabilization; but all is
raised from thewave. In particular, M is increased rela- surface
and is directed toward the
13
-
300
W =500 KT
250
U-th = 0.28 rn/s(loose sand)
~.200
E 150C0.t 04 /
4)
W 100 1h=07ml
50 (desert pavement) N
01 11 I0 200 400 600 800 1000
SHOB (ft/KT/3)
Figure 5. Net sweepup mass as function of burst altitude.
14
-
350 - SHOB = 50 ft/KT"13
-- -SHOB =250 ft/KT 1/3 U-t U.= 0.28 rn/s
300- 0
2 5 0 -.040U 'th = O .4 5 rn /s
UiCn
E
o150 U 'th= 0. 78 rn/s
100 - 0 0000 00U-th= 1.36 rn/s
500 600 700 800 900 1000
Yield, W (KT)
Figure 6. Net sweepup mass as function of yield.
15
-
00
Z U)
0
co o ' 0II - 0
0i
0 00 f00LO 0L00 IU
o CJ~t
Iw)3j sie dnem AIII3
I * 16
-
pedestal.) Unlike the sweepup mass, the soil has a two-layer
structure: A thinhowever, there is no "crossover" with in- desert
pavement veneer consisting ofcreasing threshold velocity; the
sweepup large pebbles (tens of millimeters to aradius for a 500 ft
SHOB burst is always centimeter or two in diameter),
overlyinglarger than for detonations at lower alti- a deeper layer
of finer material-typicallytudes (at least until the cutoff at U,,
h - sand or sandy loam imbedded with grav-
el. This desert pavement is usually suffl-3.5 m/s is reached).
This is as we would cintopentwdeosnofheieexpet fr aMachref-ctd
shck.It im- cent to prevent wind erosion of the fine
expect for a Mach reflected shock. It sim- particles for all but
the strongest naturalply indicates that as bursts occur at winds;
in a nuclear environment, howev-greater heights above the surface,
more er, it is easily removed, as has been ob-of the kinetic energy
is converted into served following bursts over Yucca
Valleyhorizontal dynamic pressure. The rela- [Lamar, 19621. It
therefore seems likelytionship between RE on SHOB is illus- that
nuclear sweepup over desert pave-trated in more detail in Fig. 8.
Unlike the ments may proceed in two stages: A firstsweepup mass M
(Fig. 5). we find that RE stage during which only the large
par-varies linearly with SHOB. ticles comprising the top layer
layer are
removed, followed by second, more vigor-Finally, in Fig. 9, we
show the variation ous stage during which the now-exposedin RE as a
function of yield. Again, the underlying soil is scoured. Thus,
moredependence is linear, with the greatest mass may ultimately be
lofted than ifsensitivity found for the most erodible only the
heavy top layer were present.soils. However, when expressed in
terms
of sweepup area (,-r RE 2) , this sensitivity To test whether
this two-stage processcan significantly increase the net sweep-
disappears. For example. from Fig. 9, we up mass, we have
modified our model tofind that a I-MT burst always sweeps an
account for the presence of desert pave-area about 1.6 times larger
than a ment over a fine soil. We assume that500-KT detonation at
the same altitude, the surface is initially covered with
aregardless of soil type. single layer of pebbles with mass
modal
diameters Dm = 1 cm. To this layer we4.4 NEVADA TEST SITE SOIL.
assign a threshold shear velocity U.ih =
1.36 m/s. This value is consistent withAll of the results
presented so far have the empirical relation for dry,
disturbedimplicitly assumed that the soil proper- desert soils
(Gillette et al., 19801ties are independent of depth. Thus wehave
assumed that the threshold shear U = 0.43 + 0.93 Dm (11)velocity
remains constant throughout Uth 0 9the period sweepup is occurring.
For where Dm is in centimeters. Assumingmany agricultural soils,
which have a the particles are spherical and have adeep, well-mixed
upper layer of topsoil, mass density 2.0 x 103 kg/iM3 , we
calcu-this is an appropriate assumption. But late the areal density
of the pebble layermany natural soils are not so homoge- to be 10.5
Ap kg/m 2, where 0 < A :5 1.0neously structured. The Yucca
Valley re- is the area fraction of ground actuallygion of the NTS
is an example. Soils in covered by pebbles. (We estimate Al l
most of th4s area are representative of"wind-stabilized"
alluvium from which 0.3 for Yucca Valley.) Setting U.th = 1.36
most of the erodible (i.e., small) surface m/s in Eq. 8 and
using Eq. 9. the time-elements have long since been removed
dependent pebble mass removed fromby natural wind processes. As a
result, each concentric ring around ground zero
17
-
10
0.28 (ose
0.h .5 o
Uw 4 0.78 (loose loam)
Ui U-th = 1.36 rn/s (desert pavement)
0
SHOE (ft/K -p,) 1 0
Figu r 8. ffective sw eePup radius as fun ct i0 , Of burst
altitude .
-
10SHQ8 : 5 Oft/KT 1/3
U-th 0.28 fr/sS6
&L.M.N'N .U
UAMMM th 0.5~ rnLU
*O 0
W000
piur 9. ffectv sweePuP radlius~ as functonofYild
19~ecI
-
is calculated. If, before the sweepup (3) an "infinitely deep"
pebble layer forphase ends, we find the total mass re- which U h
remains fixed at 1.36 m/smoved has exceeded the critical
density10.5 Ap kg/iM2, we assume that the throughout the
calculation. The results
pebble layer has been completely re- are presented in Table 2.
We find desert
moved from that ring. We then "instanta- pavement to be
surprisingly more stabi-
neously" reset U. to a lower value to lizing than expected. Only
when the
th pavement overlies loose sand and issimulate the exposure of
the underlying sparsely distributed (Ap = 0.3) do we findfine
particles, and proceed with the cal- an enhancement in sweepup mass
in ex-culation until sweepup ends. cess of 10 percent. This is in
spite o.' the
fact that we compute complete removalWe have computed the net
sweepup of the pebble veneer (for A - 0 3) out tomass for a 50 ft
SHOB burst at two approximately 425 ft/KT1IP range ( - 1.4yields
(500 and 1000 KT) over three dif- km for a 1-MT burst). This is
equivalentferent desert pavement configurations: to nearly
one-quarter the entire sweepup(1) A single pebble veneer over
highly area. However, the most significanterodible sand (U.th =
0.28 m/s), (2) a scouring of the underlying soil is re-
single pebble veneer over an Intermedi- stricted to ranges much
closer to groundzero; thus the net sweepup mass Is pro-ately
erodible soil ( Uth = 0.45 mis), and potoaeyrdc.
th portionately reduced.
Table 2. Sensitivity of sweepup mass to desert pavement cover
for 50 ft SHOB burst.
Sweepup Mass, M(kt)
Threshold ArealShear Velocity Pebble Pebblesof Underlying Yield,
W Cover, Pebbles Overlying Difference
Soil (m/s) (KT) Ap Only Fine Soil (%)
0.28 500 0.3 60.09 65.77 +9.420.5 60.09 63.67 +5.921.0 60.09
62.31 +3.66
1000 0.3 117.20 130.30 +11.180.5 117.20 125.70 +7.251.0 117.20
122.40 +4.44
0.45 500 0.3 60.09 63.90 +6.340.5 60.09 62.36 +3.781.0 60.09
60.10 +0.02
1000 0.3 117.20 126.20 +7.680.5 117.20 122.70 +4.691.0 117.20
120.40 +2.73
20
-
These results would be drastically differ- derlying soil; the
results are indicated inent for non-ideal surfaces when thermal the
figure. (Our choice U.th = 0.45 m/s islayers and precursors are
accounted for.
The resultant elevated dynamic pressur- somewhat arbitrary; it
probably underes-
es would likely remove the pebble veneer timates the dust pickup
at the NTS since
much sooner and to a greater distance some of the desert
pavement was broken
from ground zero. The net sweepup by pre-shot construction and
traffic.)
mass would therefore be higher. This is These results emphasize
that, comparedthe observation of to most dry barren or semi-barren
dryLamar (1962), who found near complete surfaces, Yucca Valley
soil is not as
removal of the desert pavement out to at readily eroded. This is
due to the stabi-
least 600 ft/KTI / 3 from ground zero fol- lizing effect of the
desert pavement
lowing shot SHASTA (W = 16.5 KT, pebble cover. Most other bare
soils-for
SHOB = 196 ft/KTI / 3) in Yucca Valley. example, agricultural
soils during a dry
Separate evidence, however, indicates winter or immediately
after plowing orthat this shot did not produce a strong
harvest-actually produces more sweep-precursor sLiner et al., 1975.
up than the Yucca Valley surface. Forprecursor NORMAInE et aASS.
1example, for detonations at 50 to 500 ft
4,5 NORMALIZED SWEEPUP MASS. SHOB over bare loam surfaces (Ut h
=
Figure 10 shows the variation in sweep- 0.78 m/s), between 1.3
and 2.2 timesup mass as a function of threshold ve- more dust would
be raised. On the otherlocity normalized by that calculated for
hand, if the surface were heavily vege-Yucca Valley, NTS. To
compute the nor- tated (U > 3.5 m/s), the sweepup ismalization
factor MNTS, we adopted the th"two-layer" model described above
with reduced to anywhere from zero to aboutAp = 0.3 and U.t h =
0.45 m/s for the un- 50 percent of its NTS mass.
21
-
0
Jo
0 T-- I9 LO 0U') C~ LO 4
e rl
0 I0
-0-00
I o LO CJLI) ISi "/I-wdd em ~ILwO
22,
-
SECTION 5
IMPLICATIONS FOR TARGET AREAS
Surfaces in target areas vary widely re- - A crop or grass cover
may be suffi-flecting differences in soil type, topogra- cient to
completely suppress sweepupphy, moisture levels, and vegetation
from a 500 KT airburst if the SHOBcover. Most real target surfaces
do not is greater than 500 ft/KT" /3 (Fig. 4).resemble the Nevada
desert, nor do they Thus late summer is the least vulner-remain
invariant throughout the year. able time of year for sweepup; this
isSmall differences in surface properties when crop and grass
densities arecan lead to large changes in dust sweep-
greatest.up.
e There exists an optimum burst alti-The real soil sweepup model
we devel- tude between SHOB = 80 to 100 ft/oped used a single
parameter, the KT / 3 at which the sweepup mass isthreshold
velocity, to account for soil minimized over bare soils.
Burststype, moisture, and vegetation cover, detonated below this
altitude or be-Clearly this is a simplification, but one tween 300
and 400 ft/KTI / 3 tend tothat nonetheless accounts for exper-
maximize dust production (Fig. 5).imental data on low-speed
scouring ofreal soils. In extending this analysis to For a fixed
SHOB, sweepup massnuclear sweepup, we recognize that sev- Ten to
ith Isgeral potentially important physical pro- yield. The
sensitivity to yield is great.cesses are treated inadequately or
not at est for the most erodible soils (Fig. 6).all. Inclusion of
(a) non-ideal shock ef-fects, (b) blast and thermal modification
The effective sweepiup radius in-of surface properties, (c) uneven
terrain creases with increasing burst altitudeeffects, and (d)
post-positive phase blast and yield, and is most sensitive towinds
would no doubt alter the results surface conditions over highly
erod-somewhat. We anticipate that each of ible soil (Figs.
7-9).these processes modifies the real soil * Bare, dry
agricultural soils (com-corrections we calculate, nevertheless,
posed primarily of loam) produce upthe conclusions indicatc: to 220
percent more sweepup mass
than a desert pavement surface typi-*Targets located on cropland
have the cal of the NTS (Fig. 10).
greatest dust producing potential,since the surface tends to be
bare at Our results also imply that sweepupleast part of the
year-especially dur- may not be uniform even within a singleing the
spring plowing and immedi- target area. Intercontinental
Ballisticately after harvest in the autumn Missile silo fields are
quite large, typical-(Figs. 1 and 2). Moreover, some por- ly
covering an area on the order and 104
tion of the land remains bare (i.e., km 2 in the U.S. and
somewhat less infallow) all year around. For example, the Soviet
Union. Surface conditionsin U.S. target regions, typically one-
within an area so large are not necessar-fourth the area devoted to
crops is ily uniform. A burst over one portion of afallow at any
given time [North Dako- silo field could yield a much differentta
Agricultural Statistics Service, sweepup amount and scour an area
con-19881. siderably larger or smaller than a burst
23
-
in another portion of the field. Fratricide 0.78 m/s, our
results indicate a maxi-probabilities could thus be highly vari-
mum sweepup efficiency of about 0.16able. Tg/MT for a 500-KT low
altitude burst,
Figure I I depicts a U.S. target area. ranging up to = 0.30
Tg/MT for a I-MT
Aside from isolated urban areas and bo- detonations. In
addition, we calculate
dies of water, most of the land shown maximum sweepup radii
between 3 and
here is either planted (primarily with 4 km from the burst
point-roughly one-
wheat, oats, and barley) or is tall-grass third to one-half the
mean spacing be-
wildland. Yet the soil upon which this tween silos. Smaller
sweepup radii and
vegetation grows is not the same across lower efficiencies are
to be expected from
the entire region; roughly half the silos strikes against those
silos located on
are located on loamy soil which is well- moist or poorly drained
soils, or follow-
drained and hence dry (except for peri- ing attacks during less
vulnerable times
ods immediately after a rainfall or in of year such as summer or
when the
irrigated zones). Thus, assuming U~th surface is snow-covered or
frozen.
Scale: J Moist loam1 c 14 km R 4I VIIE2 Fine i< 100 urn)
Deeo (- 20 cm)E _'Well-drained loam
SDI * eepf20cmt
I=Poorly.drained loamRockyShallow K< 20 cm)
ete sand
Source: Aandahl [1982]; Omodt et al. [1968].
Figure 1 1. Soils in the Minot AFB, North Dakota ICBM silo
area(dots indicate silo locations).
24
-
SECTION 6
CONCLUSIONS
We find that the threshold shear velocity completely suppress
sweepup. By ex-provides a useful quantitative measure trapolating
our results to real soil condi-of the susceptibility of a surface
to nu- tions in target regions, we expect evenclear sweepup. Wide
variations in this larger variations in sweepup mass couldparameter
occur naturally with seasonal result under attack conditions. We
findand regional differences in vegetation that sweepup is minimal
as long as thecover, soil moisture, soil type, and land vegetation
cover remains intact; at highuse. We find that such variations can
overpressures or high thermal fluxes,lead to large changes in the
initial the stabilizing influence is diminished.sweepup mass raised
by a low altitude The threshold velocities at which
plantairburst-particularly over surfaces lodging, breakage, and
uprooting occurwhich are dry and minimally vegetated, are not yet
established, but it is never-When vegetation is present, the
surface theless clear that sweepup is greatly re-is strongly
stabilized; in fact, a dense duced.agricultural cover can in some
cases
25
-
SECTION 7
LIST OF REFERENCES
Aandahl, A. M., Soils of the Great Plains, and Natural, Sources
and Transport, NewUniversity of Nebraska Press, Omaha, York Academy
of Sciences, New YorkNebraska, 1982. City, 1980.
Alderfer, R. B., "Soil," McGraw-Hill Ency- Gillette, D. A.,
"Threshold Friction Velo-clopedia of Science and Technology, Vol.
cities for Dust Production for Agricultur-12, McGraw-Hill, Inc.,
New York City, al Soils," J. Geopyhs. Res., Vol. 93, 1988,1977. pp.
12645-12662.
Bacon, D.. P., T. P. Dunn, and R. A. Sar- Gillette, D. A., et
al., "Threshold Veloci-ma, Late-Time Cloud Modeling, Vol. 1: ties
for Input of Soil Particles into the AirCases N1-N6, Science
Applications Inter- by Desert Soils," J. Geophys. Res.,
Vol.national Corporation, McLean, Virginia, 85, 1980, pp.
5621-5630.SAIC-88/1856, 1988. Gillette, D. A., et al., "Threshold
Friction
Bagnold, R. A., The Physics of Blown Velocities and Rupture
Moduli for
Sand and Sand Dunes, Methuen and Crusted Desert Soils for the
Input of Soil
Co., Ltd., London, 1941. Particles Into the Air," J. Geophys.
Res,,Vol. 87, 1982, pp. 9003-9015.
Brode, H. L., Airblastfrom Nuclear Gillette, D. A. and K. J.
Hanson, "SpatialBursts-Analytic Approximations, Pacific- and
Temporal Variability of Dust Produc-Sierra Research Corporation,
Los An- tion Caused by Wind Erosion in thegeles, California, PSR
1419-3, 1987. United States," J. Geophys. Res., Vol. 94,
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