Palynology and meteorology

Palynology and meteorology

Review of Palaeobotany and Palynology Elsevier PublishingCompany,Amsterdam-Printedin The Netherlands PALYNOLOGY AND METEOROLOGY F.H. SCHMIDT Royal N...

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Review of Palaeobotany and Palynology

Elsevier PublishingCompany,Amsterdam-Printedin The Netherlands

PALYNOLOGY AND METEOROLOGY F.H. SCHMIDT Royal Netherlands Meteorological Institute, De Bilt (The Netherlands}

(Received August29, 1966)

SUMMARY The deposition of small particles, suspended in the atmosphere, on the surface of the earth is governed by two mechanisms, turbulent diffusion and washout by precipitation. The effect of both depends on atmospheric conditions as well as on the properties of the particles that are deposited. The results are shown of computations with respect to the deposition of particles originating from a point source; in these computations the atmospheric stability and the intensity of precipitation are the most important par~imeters. It appears that the effect of particle dimensions is highly significant in the case of dry deposition during stable atmospheric conditions but much less so during unstable conditions. Further the effect of precipitation, even the effect of slight drizzle, may be an order of magnitude greater than that of turbulent diffusion. In explaining pollen spectra, account should be taken of the frequency with which stable and unstable conditions have occurred during the deposition, as well as of the intensity of precipitation.

INTRODUCTION The spread of pollen grains through the atmosphere is a meteorological phenomenon governed by meteorological conditions. One may distinguish between two meteorological processes that influence the displacement of pollen grains before their ultimate deposition on the ground: diffusion and wash-out. The extent to which these processes influence the displacement depends on the properties of the atmosphere as well as on the properties of the particles that are deposited. Both meteorological influences shall be discussed and we shall try to evaluate their effect on particles such as pollen grains and spores. Further, we shall make an estimate of the degree of influence each mechanism has on the spread of these particles. Rev. Palaeobotan. PalynoL, 3 (1967) 27-45

27

T H E MOTION OF PARTICLES IN I H E ATMOSPHERE

Material that is brought into the atmosphere, e.g., pollution escaping from a chimney or pollen grains liberated into the air, is subject to three mechanical influences: (a) The material is transported in the direction in which the mean wind blows. In meteorology, winds are indicated by the direction from which they blow. (b) When material that is brought into the atmosphere consists of solid or liquid particles that have a greater density than the surrounding air, which is always the case, these particles fall with a terminal velocity that depends on their dimensions and their densities. If their diameters are smaller than, say, 60/~, the terminal velocities which they attain in a very short time, is given by Stokes' wellknown law: (1)

vt -= (2/9)r2ogfil

where r is the radius of the particle, assumed to have a spherical shape; 9 its density; g the acceleration due to gravity and ~/the viscosity of the air. Taking equal to the density of water, we find under normal atmospheric conditions the relation between the radius and the terminal velocity of particles in the size range of pollen grains as shown in Table I. For larger values of the radius corrections must be applied to Stokes' velocities, e.g., a factor 0.6 for r ::= 100/z and ~ == 1 g/cm 3 leading to a terminal velocity of 73 cm/sec instead of 123 cm/sec according to Stokes. It can be stated, that the terminal velocity of pollen grains is always much below 1 m/sec. (c) If only the influences (a) and (b) were present, pollen would leave their source along a straight line, inclined at an angle arctan(vt/u) to the horizontal, u being the windspeed. Consequently, apart from an initial spread at the moment of liberation, all the pollen grains escaping from a point source, from a single tree, for example, would reach the earth's surface at a single point. Since this is not in accordance with experience, as even pollen grains originating from a very small area are deposited over an extended area, a special mechanism must exist that causes a significant additional spread. This mechanism is atmospheric diffusion which is due to the irregular turbulent motions in the atmosphere

TABLE I TERMINAL VELOCITY OF PARTICLES IN THE MICRON RANGE, W I T H DENSITY 1 G/CM 3

r(/z) vc (crn/sec)

28

5 0.30

10 1.20

15 2.70

20 4.80

25 7.50

30 10.90

Rev. Palaeobotan. PalynoL, 3 (1967) 27-45

t,O kts I

%

Fig.1. Irregularity of horizontal windspeed due to turbulent motions.

I

V

,J

u,

/

Fig.2. Irregular turbulent wind components u', 1," and w' are superimposed on the average windspeed U.

(Fig. 1 and 2). These irregular motions cause a spread of the material brought into the atmosphere. This can be understood by realising that two noncoincident particles, belonging to a cloud of material, will drift further apart with time owing to the difference between the turbulent motions in their respective environments. The structure of such a cloud of particles, whose terminal velocity is tentatively assumed to be zero, can be described by an expression of the form:

Z(x,y,z) =

(2z08/,Q~rx~ucrz exp

--

q- ~~y U- +

(2)

(see, e.g., PASQUILL, 1962). In this relationship Z(x,y,z) denotes the concentration or density of material at the point x, y, z at a fixed time. Q is the total amount of material present, which follows by integration: Rev. Palaeobotan. PalynoL, 3 (1967) 27-45

29

f f j

,13

From the exponential factor it follows that the material is assumed to be normally distributed in the three directions with az, ~ry and ~z the three standard deviations that characterize the distribution. The spread of the cloud is now introduced by taking ax, ~ry and az to be functions of time, t. If the cloud as a whole moves with the wind, this can be allowed for by substituting x x0 -! u ( t - to), t0 being the time at which the centre of the cloud was in (x0, 0, 0). The expression l\)r Z(x,y,z) can be transformed so that it relates to the diffusion of material released from a continuous point source:

o Z(x'Y'Z) = 2JzUO'y~rzexp

[

Ye z2-)] (-; -t-- r

(4)

where the positive x-axis is taken in the direction of the wind's velocity and where Q now denotes the material released per unit time. In equ.4 windspeed u is taken independent of z which is not correct in the lowest few hundred meters of the atmosphere. Allowing for a variation of windspeed with height complicates the computations largely (see, for example, Sm~u, 1965). It is also possible to write down an equation for the concentration of material coming from a continuous linesource or from an area. We shall consider here the continuous point source as it is the most simple one to handle, and quite adequate to illustrate the effects of atmospheric diffusion, relevant to our problem. The principal difficulty in treating the diffusion phenomenon lies in finding the dependence on time of a v, the width and az, the height of the "plume" that escapes from the source. In the case of the continuous point source the treatment is easier, in so far that t can be replaced by x / u where u again denotes the mean windspeed. This substitution is responsible for the factor u in the denominator of the expression for Z(x,y,z). Various methods have been applied to connect a u and az with x, the best method probably being the one introduced by Pasquill and Hay (see PASQUILL. 1962), who based the relation on a direct connection with the variations in wind direction and the vertical stability, the latter being a measure for the vertical spread. Vertical stability in the atmosphere depends wholly on the vertical temperature distribution. As long as no condensation of water vapour takes place, the relevant layer is unstable only if the temperature decreases more rapidly than by 1 °C/100 m of increasing height. High stability is present when the temperature increases with increasing height (inversion). According to Hay and Pasquill, it is possible to define the rate of diffusion of material for six stability classes, A to F, with stability increasing from A to F. On land, A only occurs on summer days when wind speeds are small and insolation is large, whereas F occurs during nights with 30

Rev. Palaeobotan. Palynol., 3 (1967) 27--45

strong radiational cooling. Diffusion is much stronger during unstable situations than during stable situations. This is principally due to the fact that vertical irregularities in the motions of small parcels of air are intensified during unstable situations and more or less suppressed during stable situations. As vertical and horizontal motions are interconnected, turbulent motions in all directions will develop more strongly for a given layer as the instability of that layer increases. This means that the dilution of a cloud or plume of material in the atmosphere will be greater the more unstable the relevant layer is. So that, starting from a point source, tru as well as trz increase more rapidly in an unstable than in a stable atmosphere. It is possible to apply the method that was delineated here in a graphical way (BRYANT, 1964). It is also possible to express the relationship between tr and x by means of functions. It is common practice then to follow SUTTON (1947) and put try and trz proportional to a power of x, the value of the exponent lying between 0.5 and 1, the lower value relating to extreme stability, and the upper to extreme instability. Although Sutton's model cannot be considered as precise, especially for long distances from the source, its application, which is relatively simple, enables one to demonstrate the various aspects of atmospheric diffusion of material escaping from a point source. Sutton's model can be put in the following form:

Z(x,y,z)

=

ztCyCz ux2-n2Q

exp {

2 z-n 1 x (_~y_- x + ~ __z- z2 )

}

(5)

Obviously, 2try2 has been replaced by C2yx 2-n and 2tr2zby C2z x 2-n, where Cv and Cz are generalized diffusion coefficients, larger for unstable than stable situations, and 2--n lies between 2 and 1, or n between 0 (extremely unstable) and 1 (extremely stable). It is preferable to distinguish between two values of n, notably nv and nz (see SCHMIDT, 1960), but the effect of this refinement is only small. The delection of 2 in the denominator of the exponent results in the disappearance of 2 in the denominator of the factor standing before exp. The factor 2 in the nominator indicates that the earth's surface is considered to be a perfect reflector of the material that is diffused. This assumption is certainly not correct in the case of spores which have a

TABLE II SUTTON'S CONSTANTS FOR STABLE~ NEUTRAL AND UNSTABLE STRATIFICATION

Stable Neutral Unstable

n

C~

C~

0.35 0.25 0.15

0.10 0.20 0.30

0.07 0.12 0.17

Rev. Palaeobotan.PalynoL, 3 (1967) 27--45

31

terminal velocity and are partly deposited, but it is difficult to find a better approximation (CHAMBERLAIN. 1955). All in all the following discussions have no more than qualitative significance but, nevertheless, they are supposed to give a correct idea of the mechanism of pollen-grain deposition. As to the numerical values of" the various constants, Table II should be considered.

THE DIFFUSION OF PARTICLES HAVING A DEPOSITION VELOCITY

In the case of pollen grains or spores which have a deposition velocity, we have to combine the effect of gravity with that of diffusion. Generally speaking it is not obvious that diffusion is uninfluenced by gravity. A particle that falls through a turbulent field will not move with the eddies that cause the diffusion but will pass these eddies, rather rapidly. The result is that a cluster, for instance, expands more slowly the larger the terminal velocity of the particles, the effect being greater the smaller the initial size of the cluster (S~ITH, 1959). Since the terminal velocities of pollen grains are small, seldom more than 10 cm/sec and mostly less than 5 cm/sec (GREGORY, 1961) we shall neglect this point. Following CHAMBERLAIN (1955) we put the deposition equal to: co(x,y)

vgz(x,y,o )

(6)

Where vg is taken equal to vt, introduced above. Now the effect of deposition on Sutton's model is that Q will decrease gradually with increasing distance from the source: +co

...... ~ ,o(x,y)dv

(7)

--oO

Integration gives: Q=

Q0exp

-

nu\/~cz j

where Q0 is the actual production of the source per unit time. (Similar results have been obtained already by Margaret F. Gregory.) The deposition in the axis of the plume with the source lying at zero height is given by:

o)(x,y :

0) :

vgz(x,3..... 0,0)

2Qov,

[__ 4_v~i!e_ _] nu~/~zCz ]

. . . . z ~ z - U X ~ _ n - exp ~

(9)

Fig.3 and 4 give the value of o)(x,y :: 0), for a point source at ground level, per unit value of Q0 during a windspeed of 5 m/sec for stable and unstable atmos32

Rev. Palaeobotan.PalynoL, 3 (1967) 27-45

10

~ -""--"'-~ ~ . - .

--

1.00 0.50

~

0.10 0.05 10 -1 5.00 10-2

10-3

\

[. . . . . 10

~

I

I

100

1000

10 L'

Vg=lO.O0

cm/sec _J 10 5 m

Fig.3. Deposition of particles, in terms of the deposition of particles with vg = 1 cm/sec as a function of distance from the point source. Windspeed 5 m/see. Stable atmosphere.

10Vg=5.0 c m / s e c

1.00 --

0.50 10.00 0.10 0.05

10 -1

10-2

10-3 f. 10

I 100

I 1000

f 10 4.

I 10 5 m

Fig.4. The same as in Fig.3. Unstable atmosphere.

pheres, respectively, a n d for d e p o s i t i o n velocities o f 0.05, 0.10, 0.50, 5.00 a n d 10.00 c m / s e c in terms o f the d e p o s i t i o n a m o u n t o f particles with vg ---- 1 cm/sec. It a p p e a r s t h a t the d e p o s i t i o n o f particles with vg > 1 c m / s e c is stronger close t o the source a n d r a p i d l y decreases with g r o w i n g distance whereas: Rev. Palaeobotan. Palynol., 3 (1967) 27-45

33

lO-3 [_ 1 0 3 ~ ~ 10-4 10-5 L.

0

0

10-6 10-7

10-8 ~10-9 ~ 10-10 ~ 10_1i 50 L 10

L 100

.......

......

L 1000



......

10 ~

100 •

5103 lO/+

10 5 m

Fig.5. Deposition rate as a function of distance from the point source and the ratio of windspeed to deposition speed (u/vg). Stable atmosphere. 100. 10-L' _ 500 ~

10 -6 10 -5 i0-7

5.10

50

10 -0

I0 -9

10-10 10-11 10-12

103 10L, I

I

I0

100

_ _

I

1000

1

10 ~

J

105 m

Fig.& The same as in Fig.5. Unstable atmosphere. ~o(vg < 1 cm/sec) o)(vg = 1 cm/sec) is < 1 close to the source but increases gradually with increasing distance. The effect is greater during stable stratification than it is in an unstable atmosphere. 34

Rev. Palaeobotan. Palynol., 3 (1967) 27-45

1

r

lore

100 200

10-1 500

1000 I

/

t0-2 I

2000

1'0/, I

0.05

I

0-10

L_.

I

0.5

1.00

I

10,0 cm/sec

Fig.7. Spectrum of particle size, expressed as deposition velocity vgfor various distances from the point source and normalized to 1 for vg = 1 cm/sec. Stable atmosphere. Fig.5 and 6 give the amount of deposition along the x-axis as a function of distance from the point source and for values of the ratio u/vg between 50 and 104. Fig.7 and 8 give a picture of the particle spectrum at various distances from the point source, again normalized to a deposition for particles with vg = 1.00 cm/ see and again, as in Fig.3 and 4, for a windspeed of 5 m/sec. It is clear, with Fig.7 referring to a stable atmosphere and Fig.8 to an unstable one, that especially in the stable case there is a significant dependence of the particle spectrum on distance, the maximum in the spectrum shifting to particles with a smaller deposition velocity as the distance from the source increases. In an unstable atmosphere, the dependence of the spectrum on distance is qualitatively the same as in a stable atmosphere but much less pronounced. From the computations it appears that the deposition velocity vg, which is connected with the maximum deposition at a certain distance from the source, shifts to smaller values with decreasing windspeed. Table III gives the value of vg at a distance of 200 m from the point source, and the value of the maximum deposition itself (expressed in the deposition for vg ---- 1.00 cm/sec) for stable and unstable atmospheres, and for windspeeds of 10, 7.5, 5 and 2.5 m/sec. Increasing windspeed leads to a more pronounced variation of deposition

Rev. Palaeobotan. Palynol.,3 (1967) 27-45

35

/

]

.,Or

00~ \

\

\ \

\ \

O0"t I

5"0 l

'~J#qdsotu:l~ ziqe~suFl

L-

~0"0

"L'8!~I u! se otues oqj~ "8"~!~I

OFO J

-t

t"q

~D

i

',0

TABLE HI DEPOSITION VELOCITY Y~ AND MAXIMUMDEPOSITION FOR X ~---200 M, VARIOUS VALUr,S OF U AND STABLEAND UNSTABLESTRATIFICATION

Stable

Unstable

u ( m/sec )

v¢ ( cm/sec )

w(va) w (1.00)

vg ( cm/sec )

w(vg) w (1.00)

10 7.5 5.0 2.5

4.3 3.2 2.5 1.7

2.00 1.10 1.26 1.00

7.6 5.7 3.8 1.9

3.19 2.54 1.82 1.18

250%,,

200

150

100

u*-- /u]

50

olI

I

[

I

I

1 2 3 4 5

I

I

10

15

I

20 m/sec /

Fig.9. Distribution of windspeed above 1 m/sec, u, in De Bilt (The Netherlands).

Rev. Palaeobotan. Palynol., 3 (1967) 27-45

37

with varying deposition velocit3. From the examples treated so far. it will be clear that a knowledge of windspeed and stability is of great importance when trying to draw conclusions with respect to the distribution of vegetation from pollen analyses, a point which amongst others has been stressed quite recently by TAU[~ER (1960). With respect to windspeed, it follows from the equation for the spread of material delivered by a point source that 1~it has to be taken into account. Generally, considerations are based on the application of the average windspeed but from Fig.9, referring to the windspeed of the central meteorological station in The Netherlands (De Bilt), it can be seen that this procedure may lead to erroneous results. The average windspeed in De Bilt over a certain period was 4.2 m/sec but the average of 1/u anaounted to 0.3, i.e., the mean windspeed relevant to diffusion problems equalled 3.3 m/sec. On the other hand one should take account of the ratio in which stable and unstable situations occur. Fig. 10 shows the percentage of unstable cases (A and B according to Pasquill's nomenclature) for various wind directions for a meteorological station in the east of The Netherlands, during daytime for the three summer months. It appears that when the wind is easterly almost 70 % of the hourly observations made during daytime point to unstable conditions, whereas this percentage is about 20 for southwesterly winds.

100O/o _

m

50

r-

{

1

0 • _

!

35G

]

I

90

!

J

i

180

[

[

_l

270



360 o

Fig.10. Frequency of unstable stratifications during daytime in summer on the Air Force base Twente in the east of The Netherlands, in dependence of 12 wind directions. Each indicated direction refers to an average over a total angle of 30°. 38

Rev. Palaeobotan. Palynol., 3 (1967) 27-45

360 * 15%

10'/,

5*/,

90*

270*

180'

8'/, Calm with 99./,% unstebte

Fig.11. Frequency of the 12 wind directions of Fig. 10 (outer polygon). The inner polygon shows the frequency of unstable stratifications. The numbers indicate the percentage of occurrence of unstable stratifications for each wind direction and give the same information as Fig. 10, therefore. Values for Calm are inserted in the figure.

However, these figures are meaningless if the number of the cases involving a specific wind direction is not given. Fig. 11 gives the complete information, the outer polygon showing the percentage of cases in which the wind direction was contained within an angle of 30 °: 350--360-10 °; 20-30-40 °; 50-60-70 °; etc., whereas the inner polygon gives the absolute percentage of unstable cases. The numbers at the angles of the inner polygon correspond with the percentages in the foregoing figure. The average percentage of the occurrence of unstable stratification, irrespective of wind direction, is about 40 during summer days against 30 during spring and autumn and about 25 during winter days. It is clear that one must distinguish between the various wind directions with respect to the occurrence of stable and unstable stratifications. This makes it extremely difficult to draw Rev. Palaeobotan, Palynol., 3 (1967) 27--45

39

conclusions from pollen spectra. It must be remarked here that little or nothing is known of the occurrence of stable and unstable stratifications during historical climates such as the Atlantic Period.

THE EFFECT OF PRECIPITATION

Particles that are suspended in the air may come down in precipitation. Distinction can be made between rain-out and wash-out. Rain-out takes place when the particles are already present in the cloud droplets, wash-out when the particles are caught by the falling precipitation, i.e., by drizzle or rain in our case. Most pollen grains and spores are too big to be caught by the cloud droplets, and so washout is the only mechanism that is of importance for removing them from the air. LANGMUIR (1948) developed the theory of the collision between small particles (in his paper cloud droplets) and raindrops. He introduced the so called catch efficiency, E, which is a function of the terminal velocities of both the raindrops and the small particles. E is the ratio of the area swept out by a raindrop to the cross-section of the cylinder in which the small particles are contained that collide with the raindrop. According to Langmuir, Eis always < 1 and although later investigators have mentioned the possibility of E:-~ 1 we shall follow Langmuir's original treatment of the problem and its extension by GREENFIELD(1957). The Table IV gives values of E for a number of diameters of both raindrops and particles, D and d, respectively, the particles are assumed to have a density of 1 g/cm 3. It did not seem necessary to modify the values of E by adopting different densities for the particles; according to GREGORY (1961, p.15) the density of pollen grains or spores may vary between 1.53 and 0.39 g/cm 3 with an average value of 0.92 g/cm 3. The diameters of the particles are given in microns, those of the raindrops in millimeters. Since the terminal velocities determine the value of E these velocities are added to the list of diameters of the particles so that account can be taken of other densities, the terminal velocity being proportional to density. Starting from Best's values of raindrop size distribution as a function of the intensity of precipitation, I, expressed in mm/h (BEST, 1950), it is possible to determine the average drop size, D, that has the same scavenging effect as the real drop population for the precipitation that is considered. From the rain intensity the number, n, of these average drops per unit time can be determined, and thence the fraction of particles of some fixed diameter, d, Fa,--d that is washed out: (10)

Fa,-~ - - 1 - - ( l - - Ea,-~) nt

where t is the total time during which the wash-out is working. Table V gives values for Fa,-B for a precipitation rate of 0.5 ram/h, and for 1, 60, 900, 3,600 and 7,200 sec, respectively. It is clear from this table that even drizzle will wash out almost all of the particles present in the atmosphere if the 40

Rev. Palaeobotan. Palynol.,

3 (1967) 27-45

1-o --..I

7~

y.

0.30 1.20 2.70 4.80

(cm/sec)

(I~)

10 20 30 40

vt

d

0.346 0.700 0.820 0.880

0.25

D (mm)

0.590 0.840 0.900 0.940

0.75

0.650 0.875 0.930 0.975

1.25

0.660 0.895 0.950 0.990

1.75

0.665 0.900 0.955 0.995

2.25

0.635 0.890 0.950 0.990

2.75

0.600 0.875 0.940 0.980

3.25

0.570 0.860 0.930 0.970

3.75

0.540 0.845 0.925 0.965

4.25

0.510 0.825 0.920 0.960

4.75

0.480 0.895 0.905 0.950

5.25

0.445 0.795 0.900 0.940

5.75

CATCH EFFICIENCY~ g~ AS A FUNCTION OF THE DIAMETERS OF LARGE AND SMALL WATER DROPLETS W I T H DIAMETERS O AND d~ RESPECTIVELY. THE TERMINAL VELOCITIES OF THE SMALL DROPLETS ARE ALSO GIVEN

TABLE IV

TABLE V

Fd,)j FOR VARIOUS DURAT[ONS WHF.N l Duration (sec)

d(t*)

1 60 900 3,600 7,200

2.90" 1.73. 2.33" 6.50" 8.87"

= 0.5 MM/H

. . . . . . . . . . . . . . . . . . . . . . . . 20 30 40

10

4.442.54" 3.30" 8.009.60"

10- a 10_2 10- a 10- 1 10 1

10- 4 10- 2 10- t 10- 1 10- I

4.80' 10- ~ 2.83 • 10- 2 3.51 • 10- 1 8.23 • 10--1 9.69 • 10-1

5.10- 10- 4 3.03 - 10- 2 3.70' 10 -i 8.44' 10 1 9.76. lO-1

drizzle continues for a few hours. W i t h an intensity o f 5 m m p e r h o u r the a t m o s phere is a l m o s t clean after a q u a r t e r o f an h o u r a n d d u r i n g heavy showers ( I := 50 m m / h ) it is a l m o s t clean within a few minutes. I n o r d e r to c o m p a r e the effect o f w a s h - o u t with the effect o f g r a v i t a t i o n a l d e p o s i t i o n we have to a p p l y a similar reasoning as a p p l i e d before with respect to the change in p r o d u c t i o n rate Q o f the source. Q0 is again the u n m o d i f i e d p r o d u c t i o n rate a n d we find f r o m integration o f equ.5 f r o m z = 0 to z = oo, taking: +oo Ox

Fe,-~(x,y)dy oo X

Fe,-~(x,y = 0) =

1--(1--Ea,g)

Q0 exp [ - - { 1 - - ( 1 - - E d , ~ ) " }] ~/~uCyxl--~n

(11)

Obviously the v a r i a t i o n o f w a s h - o u t with distance f r o m the source d e p e n d s on the rate o f diffusion, i.e., on the constants Cu a n d n. I n Fig.12 the t o t a l fraction o f w a s h - o u t is shown as a function o f distance f r o m the source for p r e c i p i t a t i o n intensities o f 0.5, 5.0 a n d 50.0 ram/h, c o m b i n e d with the diffusion constants o f a stable, a neutral a n d an unstable a t m o s p h e r e , respectively; particles are considered with d = 30# a n d the windspeed is t a k e n 2.70 m/sec. The d e p o s i t i o n due to gravity is also given. The w a s h - o u t curves clearly s h o w h o w i m p o r t a n t the effect o f w a s h - o u t is. The small values o f w a s h - o u t at large distances from the source are due to the fact t h a t the a m o u n t o f particles washed out increases strongly with time as shown in T a b l e V so t h a t at large distances only a small n u m b e r o f particles is left. Finally, Fig.13 shows the ratio between the fraction t h a t is washed out a n d the fraction t h a t falls o u t by gravity when it is assumed that b o t h mechanisms d o n o t influence each other. Obviously at distances t h a t d e p e n d on the rate o f stability 42

Rev. Palaeobotan. Palynol., 3 (1967) 27-45

10-3 10-/~ 10-5

~

U

10-6 10-7

1078 10-9

0.5 •

10.-10 10-11 I

I

I

10

100

1000

I

1

10 L,

10 5 rn

Fig.12. Wash-out of particles with a diameter of 30/t by drizzle (0.5), rain (5.0) and showers (50), respectively, and dry deposition of the same particles in a stable (S), neutral (N)and unstable (U) atmosphere, both in dependence of distance from the point source.

100

10-1

~0-2 I

[

1

I

10

100

1000

10~

____J

105 m

Fig.13. Ratio of wash-out to dry deposition as a function of distance from the point source. The effect of drizzle (0.5 mm/h) is compared with the dry deposition in a stable atmosphere, the effect of moderate rain (5 mm/h) with dry deposition in a neutral atmosphere and the effect of showers (50 mm/h) with dry deposition in an unstable atmosphere.

Rev. Palaeobotan. Palynol., 3 (1967) 27-45

43

in the atmosphere and that may vary between 100 m and l0 km, wash-out may be an order of magnitude greater than dry deposition. This factor greatly complicates the explanation of the proportion in which pollen grains are found.

CONCLUSIONS The pollen-grain content of various layers of the ground is governed in a complex way by meteorological conditions prevailing during deposition. Apart from wind direction and windspeed stability and precipitation are by far the most important meteorological parameters. Unfortunately nothing, or almost nothing, is known about stability and the intensity of precipitation in geological periods such as the Atlantic Period. Today the intensity of precipitation as well as the frequency of unstable situations increase with decreasing latitude, at least on the average. It is not improbable that conditions similar to those at lower latitudes which prevail to day prevailed in the Atlantic Period, in western Europe, for example, resulting in spectra that do not differ greatly from place to place and that have only been influenced by precipitation close to the source. In neutral conditions the influence of precipitation would be greatest at distances of about 1 km from the source, a result which has been applied by TAUBER (1965) when differentiating between the relative importance of deposition due to gravity and deposition due to precipitation in large lakes and in small ones. In conclusion, it might be recommended that meteorologists and palynologists intensify their cooperation when trying to investigate the past.

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New York, N.Y., 252 pp. LANGMUIR,1., 1948. The production of rain by a chain reaction in cumulus clouds at temperatures above freezing. J. Meteorol., 5: 175-192. PASQUILL,F., 1962. Atmospheric Diffusion. Van Nostrand, London, 297 pp.

SCnMtOT, F. H., 1960. On the dependence on stability of the parameters in Sutton's diffusion formula. Beitr. Phys. Atmosphiire, 33:112-122. 44

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SMITH,F. B., 1959. The turbulent spread of a falling cluster. In: F. N. FREmCmLand P. A. SI~PPAaD (Editors), Atmospheric Diffusion and Air Pollution. Vol. 6 of H. E. LANDSBERO(Editor), Advances in Geophysics. Academic Press, New York, N.Y., pp.193-210. SMITH, F. B., 1965. The role of wind shear in horizontal diffusion of ambiant particles. Quart. J. Roy. Meteorol. Soc., 91: 318-329. SUTTON,O. G., 1947. The problem of diffusion in the lower atmosphere. Quart. J. Roy. Meteorol. Soc., 73: 257-276. TAUBER, H., 1965. Differential pollen dispersion and the interpretation of pollen diagrams. Geol. Surv. Denmark, Set. II, 89:69 pp.

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