3 Measurement of Dry Deposition onto Surrogate Surfaces: A Review James S. Gamble and Cliff I. Davidson
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Department of Civil Engineering, Carnegie-Mellon University, Pittsburgh, PA 15213
A review of dry deposition measurement techniques is presented, focusing on surrogate surfaces. Detailed field data from the literature are available for three types of collectors: filter paper with rainshields positioned overhead, Petri dishes, and flat Teflon or polyethylene plates. The data suggest that deposition velocities of submicron particles increase in the order flat plates < Petri dishes < filter paper. For supermicron particles, the order is filter paper < Petri dishes < flat plates. These results are interpreted in terms of the geometry of the collector, surface roughness, and peripheral shielding of the surface. Recent c o n c e r n s o v e r acid d e p o s i t i o n have pollutant t r a n s p o r t f r o m t h e a t m o s p h e r e . i m p o r t a n t f o r several reasons: 1. Pollutant mass balances o n regional accurate d e p o s i t i o n rates as inputs.
enhanced interest in t h e study o f K n o w l e d g e o f such t r a n s p o r t is and global
scales
require
2. E c o s y s t e m e f f e c t s are related t o t h e amounts o f material d e p o s i t i n g and t o t h e s p e c i f i c d e p o s i t i o n p r o c e s s e s . 3. Reductions in air pollutant c o n c e n t r a t i o n s d o w n w i n d d e p e n d o n loss o f material f r o m t h e atmosphere.
of
sources
A t m o s p h e r i c t r a n s p o r t t o s u r f a c e s involves w e t and d r y d e p o s i t i o n processes. W e t d e p o s i t i o n r e f e r s t o scavenging during p r e c i p i t a t i o n , and may include i n - c l o u d p r o c e s s e s as w e l l as uptake o f pollutants b y falling r a i n d r o p s and s n o w f l a k e s . For particles, w e t d e p o s i t i o n o f t e n involves scavenging during f o r m a t i o n o f c l o u d c o n d e n s a t i o n nuclei o r ice nuclei. C o l l e c t i o n o f particles b y existing h y d r o m e t e o r s , as p o l l u t e d air masses s w e e p t h r o u g h clouds, may also be important. For w e t d e p o s i t i o n o f gases, d i f f u s i o n t o c l o u d d r o p l e t s o r ice crystals, w i t h subsequent chemical reactions, is an i m p o r t a n t p r o c e s s 0 ) . D r y d e p o s i t i o n r e f e r s t o t r a n s p o r t b e t w e e n and during p r e c i p i t a t i o n events. Particles may d e p o s i t by sedimentation, inertial impaction, i n t e r c e p t i o n , d i f f u s i o n ,
0097-6156/86/0318-0042S06.25 / 0 © 1986 American Chemical Society
Baboian; Materials Degradation Caused by Acid Rain ACS Symposium Series; American Chemical Society: Washington, DC, 1986.
3.
G A M B L E A N D DAVIDSON
Measurement of Dry Deposition
43
o r a c o m b i n a t i o n o f these mechanisms (2,3). Gases generally d e p o s i t by d i f f u s i o n f r o m the a t m o s p h e r e o n t o s u r f a c e s , w i t h subsequent chemical reactions (4)· Besides w e t and dry d e p o s i t i o n , r e c e n t r e s e a r c h has investigated the scavenging o f particles and gases by f o g d r o p l e t s . The l o w pH o f f o g in s o m e areas s u g g e s t s that this mechanism may be i m p o r t a n t f o r r e m o v i n g acid species f r o m the a t m o s p h e r e ( 5 - 7 ) .
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Several m e t h o d s have been e m p l o y e d t o measure a t m o s p h e r i c deposition. For example, p r e c i p i t a t i o n sampling b u c k e t s have been c o m m o n l y used in w e t d e p o s i t i o n m o n i t o r i n g p r o g r a m s (8). Fog has been sampled w i t h r o t a t i n g a r m c o l l e c t o r s (9). A l t h o u g h these techniques have r e c e i v e d s o m e c r i t i c i s m , the m e t h o d s are generally r e g a r d e d as adequate by many r e s e a r c h groups. A t t e m p t s t o routinely measure dry d e p o s i t i o n , o n the o t h e r hand, have e n c o u n t e r e d severe d i f f i c u l t i e s . Table 1 summarizes several measurement techniques currently available. Note that each method has important disadvantages w h i c h limit the utility f o r routine m o n i t o r i n g (10). One o f the simplest and m o s t s t r a i g h t f o r w a r d m e t h o d s o f measuring d r y deposition is w i t h surrogate surfaces. Table 1 identifies the primary disadvantage o f this technique: d e p o s i t i o n o n artificial c o l l e c t o r s may be quite d i f f e r e n t f r o m that o n natural s u r f a c e s o f i n t e r e s t F u r t h e r m o r e , it may be d i f f i c u l t t o calibrate s u r r o g a t e s u r f a c e f l u x e s w i t h t h o s e o n natural s u r f a c e s , since d e p o s i t i o n rates vary w i t h m e t e o r o l o g i c a l and s u r f a c e parameters in c o m p l e x ways. Nevertheless, d e v e l o p m e n t o f s u r r o g a t e s u r f a c e s f o r dry d e p o s i t i o n m o n i t o r i n g may be valuable f o r several potential uses: 1. L o n g - t e r m t r e n d s in d r y d e p o s i t i o n o n t o natural s u r f a c e s may be r e f l e c t e d , at least semi-quantitatively, t o similar t r e n d s measured w i t h surrogate surfaces. 2. Certain pollutant species may have f l u x e s o n t o natural s u r f a c e s w h i c h are r a t e - l i m i t e d by delivery f r o m the a t m o s p h e r e , and thus have d e p o s i t i o n rates w h i c h are relatively independent o f s u r f a c e characteristics. Examples include large particles, w h i c h d e p o s i t primarily by sedimentation, and nitric acid v a p o r w h i c h is highly reactive w i t h s o m e natural and s u r r o g a t e surfaces. 3. Many s p e c i f i c p r o c e s s e s o f d r y d e p o s i t i o n in the f i e l d are best studied w i t h s u r r o g a t e s u r f a c e s w h i c h can be m o d i f i e d t o suit the design o f the experiment. Examples include investigations into the e f f e c t s o f obtacle g e o m e t r y and s u r f a c e roughness. 4. Relating f l u x e s o n s u r r o g a t e s u r f a c e s t o t h o s e o n s o m e natural s u r f a c e s may be feasible f o r certain designs o f collectors. Research t o assess this possibility is n e e d e d (11). This paper addresses the use o f s u r r o g a t e s u r f a c e s t o assess d r y d e p o s i t i o n o f a t m o s p h e r i c pollutants. Several o f the designs o f artificial c o l l e c t o r s r e p o r t e d in the literature are r e v i e w e d . Published data obtained w i t h these c o l l e c t o r s are then summarized and i n t e r p r e t e d .
Baboian; Materials Degradation Caused by Acid Rain ACS Symposium Series; American Chemical Society: Washington, DC, 1986.
44
MATERIALS DEGRADATION CAUSED BY ACID RAIN
Table
I : Examples o f t e c h n i q u e s f o r a s s e s s i n g d r y d e p o s i t i o n under f i e l d c o n d i t i o n s a f t e r H i c k s e t a l . , 1980 (10)
Category: F l u x Measurements These methods use s u r r o g a t e o r n a t u r a l s u r f a c e s t o d i r e c t l y measure t h e f l u x o f the d e p o s i t i n g m a t e r i a l on a s m a l l s u r f a c e a r e a . Surrogate
Surfaces
V e g e t a t i o n Washing
Snow Sampling
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Description: - A r t i f i c i a l collectors (e.g. b u c k e t s , f u n nels, P e t r i dishes, f i l t e r p a p e r s , and f l a t p l a t e s ) s e t up i n the f i e l d and exposed f o r knowi time p e r i o d s . -Rainshields occasiona l l y used t o d i s t i n g u i s h between wet and dry d e p o s i t i o n . - S t i c k y f i l m s or other adhesive m a t e r i a l sometimes used t o minimize p a r t i c l e resuspension.
-Requires d e t a i l e d r a i n chemistry studies including r a i n f a l l and v e g e t a tion throughfall measurements. - T y p i c a l l y uses washing o f i n d i v i d u a l l e a v e s and measurement o f s p e c i e s concent r a t i o n i n wash fluid.
-Uses comparison o f species concentrat i o n s i n f r e s h and o l d e r snow. -Dry d e p o s i t i o n i n f e r r e d by d i f ference.
- D i r e c t measurement of f l u x e s . - P o s s i b l e t o extend r e s u l t s to e n t i r e foliage. -Permits chemical analysis.
- D i r e c t measurements of f l u x e s . -Particularly useful during periods of low d e p o s i t i o n fluxes. -Permits chemical analysis.
-Large s p a t i a l v a r i a tions i n deposition within foliage. -Occasionally d i f f i c u l t t o i s o l a t e depos i t i o n on s u r f a c e from i n t e r n a l p l a n t material.
-Snow s u b l i m a t i o n , m i g r a t i o n o f cont a m i n a n t s , and b l o w i n g snow may cause i n a c c u r a c i e s . -May have s m a l l d i f f e r e n c e s between l a r g e numbers.
Advantages : - S i m p l e and i n e x p e n sive. -Permits i n v e s t i g a t i o n of i n d i v i d u a l d e p o s i t i o n processes. -Permits chemical analysis.
Disadvantages : - R e l a t i o n to deposit i o n on n a t u r a l s u r f a c e s unknown. - D e s i g n and use o f a r t i f i c i a l collectors not s t a n d a r d i z e d .
Baboian; Materials Degradation Caused by Acid Rain ACS Symposium Series; American Chemical Society: Washington, DC, 1986.
3.
G A M B L E A N D DAVIDSON
45
Measurement of Dry Deposition
T a b l e I : Examples of t e c h n i q u e s f o r a s s e s s i n g under f i e l d c o n d i t i o n s ( c o n t i n u e d )
dry
deposition
Category; E s t i m a t e s of R e g i o n a l A c c u m u l a t i o n T h i s group of d r y d e p o s i t i o n m o n i t o r i n g t e c h n i q u e s a t t e m p t s to measure the a c c u m u l a t i o n of a s p e c i e s i n a r e g i o n of known s i z e o v e r a s p e c i f i e d p e r i o d of time.
Atmospheric Radioactivity
Mass B a l a n c e
Tracers
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Description: -Uses e x i s t i n g atmospheric radioactive f a l l o u t as a t r a c e r of o p p o r t u n i t y .
-Used i n watershed monitoring. -Uses a m a t e r i a l budget model f o r m u l a t i o n . -Measurements made of wet d e p o s i t i o n and w e a t h e r i n g (as r e g i o n a l i n f l o w s ) and r u n o f f (as r e g i o n a l o u t f l o w s ) for given species . -The amount of d r y depo s i t i o n i s not measured but i s i n f e r r e d by the d i f f e r e n c e of measured i n f l o w s and outflows.
-Tagged m a t e r i a l s (e.g. r a d i o a c t i v e o r fluorescent) rel e a s e d over n a t u r a l surfaces. -Samples of s u r f a c e are analyzed f o r concentrations of tracer. -airborne tracer c o n c e n t r a t i o n s above surface also measured.
-Net d r y d e p o s i t i o n i n f e r r e d f o r large area.
-Dry d e p o s i t i o n i s measured d i r e c t l y on natural surfaces.
-Dry d e p o s i t i o n not measured d i r e c t l y , - m u l t i p l e complex v a r i a b l e s (e.g. b i o c h e m i c a l and geochem i c a l r e a c t i o n s ) must be c o n s i d e r e d i n the model development. - D i f f i c u l t to i n v e s t i g a t e the i n f l u e n c e of surface c h a r a c t e r i s t i c s .
- C h a r a c t e r i s t i c s of t r a c e r may not r e p r e sent t h o s e of the s p e c i e s of i n t e r e s t , - i n s u f f i c i e n t mixing may i n v a l i d a t e a i r borne and d e p o s i t i o n measurements. - L o g i s t i c a l problems in following tracer plume o v e r l a r g e distances.
Advantages : - P e r m i t s e v a l u a t i o n of net uptake r a t e s of species for w e l l d e f i n e d ecosystems. -Long term i n t e g r a tions possible. Disadvantages : -Detailed investigat i o n of s p e c i f i c dep o s i t i o n processes g e n e r a l l y not possible. - D i s t i n c t i o n between wet and d r y deposition d i f f i c u l t . -Differences i n size d i s t r i b u t i o n s of a m o n i t o r e d s p e c i e s and background r a d i a t i o n may i n v a l i d a t e any comp a r i s o n s made u s i n g t h i s technique.
C o n t i n u e d on n e x t page
Baboian; Materials Degradation Caused by Acid Rain ACS Symposium Series; American Chemical Society: Washington, DC, 1986.
46
MATERIALS DEGRADATION CAUSED BY ACID RAIN
T a b l e I : Examples o f t e c h n i q u e s f o r a s s e s s i n g d r y d e p o s i t i o n under f i e l d c o n d i t i o n s ( c o n t i n u e d )
Category: Flux Parameterization These methods i n v o l v e t h e use o f a i r b o r n e c o n c e n t r a t i o n and r e l a t e d m e t e o r o l o g i c a l d a t a t o i n f e r the d e p o s i t i o n f l u x , r a t h e r than d i r e c t measurement o f a c c u m u l a t i o n of a s p e c i e s on s u r f a c e s .
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Box Budget
Eddy C o r r e l a t i o n
Gradients
- F a s t r e s p o n s e anemo meters measure v e r t i c a l wind component, w. -Simultaneously, r e a l time p a r t i c l e o r gas a n a l y z e r s measure con c e n t r a t i o n , C. -Mean v a l u e s removed leaving w and C . -Product w C calculated and time-averaged t o y i e l d turbulent flux of m o n i t o r e d s p e c i e s .
-Compare differences between c o n c e n t r a t i o n s a t two o r more heights. - I n f e r f l u x as Κ
- P r o v i d e s an i n s t a n t a neous e v a l u a t i o n o f d r y deposition flux.
-Fast-response sensors not needed. -Conceptually s t r a i g h t - f o r w a r d and well-studied.
-Requires fast-response s e n s o r s f o r b o t h wind v e l o c i t y and c o n c e n t r a t i o n (1 s e c ) . - S t r i c t fetch require ments .
-May have s m a l l d i f f e r e n c e s between l a r g e numbers. - S t r i c t fetch requirements.
Description: -Airborne Concentra t i o n s measured on t h e b o u n d a r i e s of a g i v e n area. - D i f f e r e n c e between i n f l o w s and o u t f l o w s , coupled with sources i n t h e r e g i o n , used to c a l c u l a t e t h e d r y deposition.
1
f
f
f
D
C
where : Κ = S p e c i e s eddy diffusivity, f u n c t i o n of atmospheric stability, surface roughness, and momentum f l u x .
Advantages : -Net S u r f a c e f l u x determined f o r l a r g e
Disadvantages : -May have s m a l l d i f f e r e n c e s between l a r g e numbers. -Requires d e t a i l e d knowledge o f a l l sources w i t h i n area. - I g n o r e s inhomogen e i t i e s of area.
Baboian; Materials Degradation Caused by Acid Rain ACS Symposium Series; American Chemical Society: Washington, DC, 1986.
3.
G A M B L E A N D DAVIDSON
Measurement of Dry Deposition
47
T a b l e I : Examples of t e c h n i q u e s f o r a s s e s s i n g d r y d e p o s i t i o n under f i e l d c o n d i t i o n s ( c o n t i n u e d )
Category: Flux Parameterization These methods i n v o l v e the use of a i r b o r n e c o n c e n t r a t i o n and r e l a t e d m e t e o r o l o g i c a l d a t a t o i n f e r the d e p o s i t i o n f l u x , r a t h e r than d i r e c t measurement o f a c c u m u l a t i o n of a s p e c i e s on s u r f a c e s .
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Eddy
Accumulation
Variance
Description: -Compare time-averaged s p e c i e s concentrations i n updrafts with those i n downdrafts.
-Measure v a r i a n c e o f s p e c i e s c o n c e n t r a t i o n , and heat (or humidity) simultaneously at a g i v e n h e i g h t and l o c a t i o n . - A l s o s i m u l t a n e o u s l y measure s e n s i b l e heat f l u x (or evapora tion) . - I n f e r F l u x of s p e c i e s , J , a s : σ
J
c
=
Η
or,
σ„
Advantages : - P e r m i t s e v a l u a t i o n of t i m e averaged f l u x e s . -Permits chemical a n a l y s i s f o r some s p e c i e s .
-No knowledge of s u r f a c e c h a r a c t e r i s t i c s o r v e r t i c a l wind v e l o c i t i e s necessary. -May use s l i g h t l y slower response chemical sensors compared w i t h eddy c o r r e l a t i o n .
Disadvantages : -Requires very p r e c i s e chemical a n a l y s i s techniques ( p r e c i s i o n = 1%) . -Requires s o p h i s t i c a t e d e l e c t r o m e c h a n i c a l systems.
-Temperature method f a i l s f o r near-neutral conditions. -Humidity s e n s o r u n r e l i a b l e and d i f f i c u l t to m a i n t a i n . - S t r i c t f e t c h requirements. - S i g n o f f l u x (up o r down) i s unknown.
American Chemical Society Library 1155 16th St. N. W. Washington, D. C. 20036 Baboian; Materials Degradation Caused by Acid Rain ACS Symposium Series; American Chemical Society: Washington, DC, 1986.
MATERIALS DEGRADATION CAUSED BY ACID RAIN
48
Design o f E x i s t i n g S u r r o g a t e
Surfaces
Many d i f f e r e n t designs o f s u r r o g a t e s u r f a c e s have been used t o measure d r y d e p o s i t i o n in the field. These include s m o o t h flat s u r f a c e s , r o u g h flat s u r f a c e s , and c o l l e c t o r s w i t h c o m p l e x geometries. Examples o f additional design m o d i f i c a t i o n s include application o f an adhesive c o a t i n g t o minimize particle resuspension, covering the surface with a film of water to study d i f f u s i o p h o r e s i s , and use o f rainshields t o p r e v e n t contamination a n d / o r w a s h o f f by precipitation. Table 2 d e s c r i b e s many o f the s u r r o g a t e s u r f a c e designs r e p o r t e d in the literature. The d e s c r i p t i o n s are listed in o r d e r o f increasing r i m height. Unless o t h e r w i s e n o t e d , these c o l l e c t o r s are generally p o s i t i o n e d horizontally, f a c i n g upward. N o t e that s u r f a c e areas range f r o m 19 t o about 5 8 0 0 c m , and have been used 0.4 m t o 2 0 m a b o v e g r o u n d . The dimensions given r e f e r t o the horizontal s u r f a c e alone, e x c l u d i n g vertical walls o r rims. Figures 1 - 6 p r e s e n t e x a m p l e s o f s o m e o f the s u r f a c e s listed in the table.
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2
It is interesting t o n o t e that the s u r f a c e used m o s t w i d e l y in the United States is the A e r o c h e m - M e t r i c s b u c k e t Since 1 9 8 2 , the b u c k e t s have been d e p l o y e d at o v e r 1 0 0 sites n a t i o n w i d e as part o f the National A t m o s p h e r i c D e p o s i t i o n P r o g r a m (NADP) (8). This m o n i t o r i n g p r o g r a m has r e s u l t e d in a sizeable d r y d e p o s i t i o n f l u x data base f o r n u m e r o u s t r a c e element and ionic s p e c i e s (12).
Data P r e s e n t a t i o n and D i s c u s s i o n The s u r r o g a t e s u r f a c e s s u m m a r i z e d in Table 2 have been used t o measure d r y deposition fluxes f o r a number of species. In many cases, airborne concentrations have been measured simultaneously with deposition rates, p e r m i t t i n g estimation o f the d r y d e p o s i t i o n v e l o c i t y v (cm/sec): d
ν
= -J/C α
Where:
Results o f For
three
those types
J = D e p o s i t i o n Rate, g / c m s e c C = Airborne Concentration, g / c m 2
studies r e p o r t i n g d e p o s i t i o n velocities are s h o w n of
surrogate
surfaces, a sufficiently
permit construction o f graphs o f v median
3
aerodynamic
diameter
of
rf
versus dp. the
large
in Table
database
3.
exists
to
In this c o n t e x t Hp is the mass
airborne
species
depositing
onto
the
surrogate surfaces. Previous w o r k has s h o w n that the small f r a c t i o n o f dominates total mass d e p o s i t i o n o f
a species (2, 3 2 , 38).
t h e r e is a relation b e t w e e n Hp and the f r a c t i o n o f p r o v i d e a r o u g h indication o f
t h e influence o f
velocity
for
a particular
surrogate
species
has
been
from
summaries o f
taken
some 5 0 0
surface.
Milford
and
particle
Davidson
size o n d r y
(39,
often
T o the e x t e n t
large particles, t h e s e
Choice o f d p
independent sets o f
large particles
for 40),
that
graphs
deposition
most which
of
these
includes
size d i s t r i b u t i o n data r e p o r t e d
Baboian; Materials Degradation Caused by Acid Rain ACS Symposium Series; American Chemical Society: Washington, DC, 1986.
in
Baboian; Materials Degradation Caused by Acid Rain ACS Symposium Series; American Chemical Society: Washington, DC, 1986.
plate
plate
Flat
Flat
20 cm d i a .
76 cm χ 76
cm
cm
cm d i a .
plate
Flat
13.3
plate
Flat
cm d i a .
cm d i a .
9.4
plate
Flat
17.6
cm χ 7.6
2.5
Dimensions
Microscope slides
Surface Type
Teflon
Teflon
FEP
FEP
1.0
10,20
T e f l o n laminated aluminum sheet Polyethylene
0.4,
1.5
1.5 m above ground l e v e l , 1.5 m above b u i l d i n g roof
Teflon
FEP
1.5
0.0
Height, m (Above ground unless otherwise indicated)
Glass
Deposition Surface Material Remarks
McDonald e t a l . , Rimless
C o n t i n u e d on n e x t
page
1982
Smith and Friedman, 1982; D o l s k e and Gatz , 1982 (21, 19) Rimless
(22)
D o l s k e and G a t z , 1982 D a v i d s o n e t a l . , 1985b (19, 20)
rim
Mounted f l u s h i n aluminum h o l d e r s , some e x p e r i m e n t s used f i x e d r a i n s h i e l d 30 cm o r 45 cm above p l a t e ( F i g u r e 2)
cm
E l i a s and D a v i d s o n , 1980; D a v i d s o n and E l i a s , 1982 (17, 18)
(13)
1.0
Raynor, 1976
D a v i d s o n , 1977; D a v i d s o n and F r i e d l a n d e r , 1978; D a v i d son e t a l . , 1985a 0 4 , 15, L6)
coated grease
Reference
0.3 cm r i m on s t a i n less steel holder, top and bottom d e p o s i t i o n measure ments ( F i g u r e 1)
Glass s l i d e s with s i l i c o n
Table I I : Surrogate Surface Designs
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Baboian; Materials Degradation Caused by Acid Rain ACS Symposium Series; American Chemical Society: Washington, DC, 1986.
L i n d b e r g and L o v e t t , 1985 (32)
Polycarbon ate
9.5 cm d i a . 1.3 cm deep
dish
Petri
Automatic r a i n s h i e l d located i n foliage ( F i g u r e 6)
—
Polethylene
9.5 cm d i a . 1.3 cm deep
dish
Petri
15-19
Mounted on a 15.0 cm J a p a r e t a l . , 1985 (30) d i a . Τ2flon-coated stainless steel plate
17
PTFE T e f l o n membrane ( Z e f l o u r , Membrana Corp.)
14.2 cm d i a .
F i l t e r paper
L i n d b e r g and H a r r i s s , 1981 (31)
Mounted on a 15.0 cm J a p a r e t a l . , 1985 dia. Teflon-coated (30) stainless steel plate
17
Nylon membrane (Nylasorb, Membrana Corp.
14.2 cm d i a .
F i l t e r paper
Located i n f o l i a g e , no r a i n s h i e l d
P a t t e n d e n e t a l . , 1982 Used a u t o m a t i c r a i n s h i e l d ( F i g u r e 4) (29)
1.0
Cellulose (Whatman 541)
25 cm χ 20 cm
F i l t e r paper
Cawse e t a l . , 1973, 1974, 1975, 1976; P e i r s o n e t a l . , 1973; I b r a h i m e t a l . , 1983 (23 -28)
Used a f i x e d 1 m χ 1 m r a i n s h i e l d 12 cm above d e p o s i t i o n surface, f i l t e r paper mounted on P e r s p e x frame ( F i g u r e 3)
1.0
Reference
Cellulose (Whatman 541)
Remarks
25 cm χ 20 cm
Dimensions
Height, m (Above ground unless otherwise indicated)
F i l t e r paper
Surface Type
Deposition Surface Material
Table I I : Surrogate Surface Designs (continued)
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