OPTICAL PROPERTIES AND THE DETECTION OF BLOWING SNOW

J . W . Pomeroy and D.H. Male

Div is ion of Hydrology Un ive r s i t y of Saskatchewan

Saskatoon, Saskatchewan Canada S7N OW0

Paper prepared f o r : "Symposium on Remote Sensing and Electromagnet ic P r o p e r t i e s of Snow and Ice' '

American Geophysical Union F a l l Meeting 11 December 1985

San Francisco, C a l i f o r n i a , U.S.A.

OPTICAL PROPERTIES AND THE DETECTION OF BLOWING SNOW

J . W . Pomeroy and D.H. Male

INTRODUCTION

A c h a r a c t e r i s t i c of blowing snow is reduced v i s i b i l i t y caused by t h e

a b i l i t y of snow p a r t i c l e s t o s c a t t e r and absorb e lec t romagnet ic r a d i a t i o n .

Severa l empi r i ca l i n v e s t i g a t i o n s of t h e l i g h t ex t ingu i sh ing c h a r a c t e r i s t i c s of

blowing snow have been publ ished (Landon-Smith and Woodberry, 1965; Mellor ,

1966; Tabler , 1984) which suggest t h a t t h i s proper ty can be used t o measure t h e

mass of blowing snow per u n i t volume of atmosphere ( d r i f t d e n s i t y ) . Recent

i n v e s t i g a t i o n s of f a l l i n g snow (Seagraves, 1984) suggest t h a t bo th t h e snow

c r y s t a l s i z e d i s t r i b u t i o n and mass concent ra t ion of f a l l i n g snow can be measured

us ing t h e l i g h t e x t i n c t i o n p r o p e r t i e s of snow.

It is t h e purpose of t h i s s tudy t o examine t h e o p t i c a l p r o p e r t i e s of blow-

ing snow f o r t h e v i s i b l e and i n f r a r e d wavelengths and t o demonstrate t h e a p p l i -

c a t i o n of t h e s e p r o p e r t i e s i n t h e c a l i b r a t i o n of a n o p t i c a l measuring system f o r

blowing snow. Schmidt e t a l . (1984) have demonstrated t h a t o p t i c a l measuring

systems a r e capable of r a p i d , continuous measurements w i t h minimal i n t e r f e r e n c e

t o t h e snow-air f l ux . A t h e o r e t i c a l l y c a l i b r a t e d system capable of measuring

both t h e p a r t i c l e s i z e d i s t r i b u t i o n and d r i f t d e n s i t y has an advantage over

empi r i ca l ly c a l i b r a t e d mass f l u x t r a p s .

PROPERTIES OF BLOWING SNOW

Blowing snow i s s u r f a c e snow which has been e n t r a i n e d and i s being t r ans -

por ted by t h e wind. The mode of t r a n s p o r t w i th in about 0.05 m of t h e s u r f a c e i s

s a l t a t i o n , which involves r e g u l a r momentum exchange between t h e p a r t i c l e and t h e

snow s u r f a c e a s w e l l a s t h e ho r i zon ta l component of t h e wind. Above about 0.05 m,

suspended t r a n s p o r t occu r s , and has been observed a t h e i g h t s up t o 1000 m i n

Western Canada. The f a l l v e l o c i t i e s of blowing snow p a r t i c l e s a r e i n t h e same

range a s v e r t i c a l t u r b u l e n t v e l o c i t i e s dur ing blowing snow. A s a r e s u l t t h e r e

is a n exponen t i a l dec rease i n t h e d r i f t d e n s i t y as he ight i s inc reased .

Blowing snow p a r t i c l e s a r e u sua l ly metamorphosed fragments of t h e s u r f a c e

snow cover and bear l i t t l e s i m i l a r i t y t o f a l l i n g snow c r y s t a l s . The snow f r ag -

ments a r e abraded dur ing s a l t a t i o n and r a p i d l y become rounded, though occasion-

a l l y somewhat e l l i p s o i d (Schmidt, 1981). During suspended t r a n s p o r t , enhanced

sub l ima t ion f u r t h e r rounds and smooths t h e p a r t i c l e s . The d e n s i t y of blowing

snow p a r t i c l e s is approximately equal t o that of i c e . Thus blowing snow par-

t i c l e s approach t h e " o p t i c a l l y i d e a l " i c e sphere more c l o s e l y than do o t h e r

forms of snow.

The s i z e d i s t r i b u t i o n of blowing snow p a r t i c l e s has been f i t t e d t o t h e two

parameter gamma d i s t r i b u t i o n f o r both suspended (Budd, 1966) and s a l t a t i n g

t r a n s p o r t modes (Schmidt, 1981; 1984). This d i s t r i b u t i o n has t h e form

where f ( P ) is t h e r e l a t i v e frequency of p a r t i c l e r a d i u s P a i s t h e d i s t r i b u - r r ' t i o n shape parameter, @ is t h e s c a l e parameter and r denotes a gamma func t ion .

The parameters a and f3 a r e a l s o def ined i n terms of t h e mean p a r t i c l e r a d i u s

- P (Haan, 1977) where r -

P =aB . r

The v a l u e of a is approximately 5 f o r s a l t a t i n g and 1 0 f o r suspended t r a n s p o r t .

The mean p a r t i c l e r a d i u s dec reases w i th he ight , t y p i c a l v a l u e s being 100 pm

near t h e s u r f a c e and 40 pm a t 2 m. The degree of t u rbu lence i n t h e wind can

cause P t o f l u c t u a t e f o r a given he ight . r

OPTICAL PROPERTIES OF BLOWING SNOW

The e lec t romagnet ic t r ansmi t t ance through a d i s p e r s i v e media is t h e r a t i o

of t h e l i g h t i n t e n s i t y t r ansmi t t ed through t h e media t o t h a t i n t e n s i t y t r a n s m i t t e d

wi thout t h e s c a t t e r i n g and abso rp t ion e f f e c t s of t h e media. Following t h e

Bouger-Lambert law, t h e t r ansmi t t ance T through an ensemble of small p a r t i c l e s

i s found from t h e l e n g t h of t ransmiss ion L and t h e e x t i n c t i o n c o e f f i c i e n t ah f o r

t h e wavelength h considered, where

The e x t i n c t i o n c o e f f i c i e n t i s a func t ion of t h e c ross - sec t iona l a r e a of p a r t i c l e s

per u n i t volume and t h e e x t i n c t i o n e f f i c i e n c y Q of t h e p a r t i c l e s . Thus, e

I n Eq. 4 N i s t h e number of p a r t i c l e s per u n i t volume of atmosphere, and

dP deno tes t h e i n t e g r a l of P over t h e r a d i u s range. r

The e x t i n c t i o n c o e f f i c i e n t can be expressed i n terms of t h e d r i f t d e n s i t y

rl by t h e fol lowing s u b s t i t u t i o n . The d r i f t d e n s i t y i s def ined as

r

L

where p is t h e d e n s i t y of snow p a r t i c l e s . S u b s t i t u t i n g t h e d r i f t d e n s i t y i n t o i

Eq. 4 and i n t e g r a t i n g over t h e p a r t i c l e r a d i u s y i e l d s

Thus, t h e e x t i n c t i o n c o e f f i c i e n t is a func t ion of n , a, 6 and A .

The v a r i a t i o n of Q wi th P and h must be def ined t o so lve Eq. 6. I n e r

c l a s s i c a l geometr ical o p t i c s Q i s considered equal t o 2.0, an approximation e

which i s on ly v a l i d f o r p a r t i c l e s t h a t a r e l a r g e wi th r e s p e c t t o t h e l i g h t

wavelength. For smal le r p a r t i c l e s Q i s a func t ion of t h e p a r t i c l e s i z e para- e

meter x = 2nP /A and t h e complex index of r e f r a c t i o n . This func t ion can be r

c a l c u l a t e d us ing t h e Mie complex angular momentum approach t o l i g h t s c a t t e r i n g

(van d e Hu l s t , 1957). However, even t h e f a s t e s t a lgor i thms (Wiscombe, 1980;

Ungut e t a l . , 1981) can r e q u i r e excess ive computing time, p a r t i c u l a r l y when

x i s l a r g e and a range of s c a t t e r i n g ang le s and s i z e parameters a r e cons idered .

Nussenzveig and Wiscombe (1980) have proposed asymptot ic approximations t o t h e

e x t i n c t i o n e f f i c i e n c y based on Mie theory. These c a l c u l a t i o n s e x h i b i t e r r o r s of

l e s s t han 0.01% when compared t o exac t Mie c a l c u l a t i o n s and a r e w e l l s u i t e d t o

a p p l i c a t i o n s where an ensemble of non-uniform p a r t i c l e s a r e considered.

Blowing snow p a r t i c l e s a r e e s s e n t i a l l y i c e spheres , f o r which I r v i n e and

P o l l a c k (1968) have c a l c u l a t e d t h e r e a l and Fmaginary components of t h e index

of r e f r a c t i o n f o r v a r i o u s wavelengths. Using t h e s e va lues , t h e e x t i n c t i o n

e f f i c i e n c y Q has been c a l c u l a t e d us ing Nussenzveig and Wiscombe's (1980) a lgo r - e

i t h m . The r e s u l t s a r e p l o t t e d a g a i n s t t h e snow p a r t i c l e r a d i u s f o r v a r i o u s

wavelengths i n Fig. 1. Note t h a t f o r X = 300 nm, Q i s w i t h i n 1% of 2.0 f o r e

p a r t i c l e s g r e a t e r than 50 urn i n rad ius . The corresponding r a d i i f o r which Q is e

w i t h i n 1% of 2.0 f o r A = 600 nm i s 95 pm and f o r X = 1.06 pm i s 168 pm. Qe a t

X = 2 pm i s never c o n s i s t e n t l y w i t h i n 1% of 2.0. For blowing snow, t h e d i f f e r -

ence between t h e geometr ica l o p t i c s and ~ i e theory Q becomes more pronounced as e

wavelength inc reases and extends t o l a r g e r p a r t i c l e s i z e s . However, a t a l l

wavelengths, t h e smal le r p a r t i c l e s e x h i b i t g r e a t e r e x t i n c t i o n e f f i c i e n c i e s t han

do l a r g e r p a r t i c l e s .

The behaviour of t h e e x t i n c t i o n c o e f f i c i e n t can be demonstrated by i t s

e f f e c t on t h e meteoro logica l v i s u a l range, a n i n v e r s e l i n e a r f u n c t i o n of a The X '

meteoro logica l v i s u a l range V is t h e maximum d i s t a n c e a t which a n "averageH eye

can d i s t i n g u i s h a b l ack o b j e c t of lo i n v i s u a l angle . Koschmieder's d e f i n i t i o n

of v i s u a l range a t a g iven wavelength (Middleton, 1952) is;

While t h e concept of "v isua l" range becomes a b s t r a c t o u t s i d e of t h e v i s i b l e

spectrum, i t i s a s tandard meteorological v a r i a b l e and a u s e f u l s u r r o g a t e f o r

t h e e x t i n c t i o n c o e f f i c i e n t .

o 20 40 60 80 100 120 140 ieo ieo zoo 220 240 zeo zeo

S N O W PARTICLE RADIUS C m i c r . >

'e 1. Mie Ex t inc t ion E f f i c i e n c i e s . Calculated f o r blowing snow us ing Nussenzveig and Wiscombe's (1980) asymptot ic approximation f o r wavelengths of 300 nm , 600 nm ---- , 1.06 pm - - - and 2.0 pm - . - . The geometr ical o p t i c s approximation i s 2.Q.

Ca lcu la t ion of V involves combining Eqs. 6 and 7 , d e f i n i n g t h e p a r t i c l e X

s i z e d i s t r i b u t i o n parameters and so lv ing f o r v a r i o u s wavelengths and d r i f t

d e n s i t i e s . Budd (1966) and Schmidt (1982) suggest f o r suspended blowing snow

p a r t i c l e r a d i i t h a t a = 1 0 is a reasonable va lue . Pomeroy e t a l . (1985) demon-

strate t h a t f o r a given P even a 50% v a r i a t i o n i n a r e s u l t s i n a n i n s i g n i f i - r ' c a n t change i n a when in t eg ra t ed over t h e p a r t i c l e s i z e d i s t r i b u t i o n . The

v i s u a l range through blowing snow as a func t ion of d r i f t d e n s i t y f o r a = 10 , a

v a r i e t y of X and t h e suspended range of P has been c a l c u l a t e d and is p l o t t e d i n r

Fig. 2. Var i a t ion i n wavelength from t h e u l t r a v i o l e t t o near i n f r a r e d r e s u l t s

i n a v i s u a l range v a r i a t i o n of between 1 .5 t o 8.3% wi th o t h e r f a c t o r s cons tan t .

However, v a r i a t i o n of t h e mean p a r t i c l e r a d i u s through i ts range f o r suspended

blowing snow r e s u l t s i n v i s u a l range v a r i a t i o n of between 52.9 and 56.2% wi th

o t h e r f a c t o r s cons tant . The mean p a r t i c l e s i z e appears t o be an important f a c t o r

a f f e c t i n g t h e blowing snow d r i f t d e n s i t y - v i s u a l range r e l a t i o n s h i p .

MP4

MPR MPR

. O 1 I I I 1 1 1 1 1 1 1 1 1 1 1 1 1 I I I -01 .05 . 10 . 50 1.00 5. 00

micr.

micr. rnior.

DRIFT DENSITY ~ ~ / r n 3 >

Figure 2. Visual Range i n Blowing Snow. - Calcula ted f o r a gamma d i s t r i b u t i o n of p a r t i c l e r a d i i a of 10 , Pr of 40, 50 and 90 pm and wavelengths of 300, 600, 1006 and 2000 nm though t h e wavelengths a r e not i n d i - v i d u a l l y d i sce rnab le . Budd e t a l . ' s (1966) obse rva t ions a r e p l o t t e d a s *.

Meteorological v i s u a l ranges ( v i s i b l e spectrum) and d r i f t d e n s i t i e s a t a

2-m he igh t were measured i n t h e A n t a r c t i c by Budd e t a l . (1966). These d a t a a r e

a l s o p l o t t e d i n Fig. 2 and correspond t o t h e t h e o r e t i c a l p r e d i c t i o n s us ing P = r

40 pm. While Budd e t a l . (1966) do no t provide t h e 7 va lue from t h e i r obser-

v a t i o n s , Budd (1966) i n d i c a t e s a n expected of 40-45 pm a t a 2-m he igh t f o r

s i m i l a r cond i t i ons . The d a t a of Budd e t a l . , while spa r se , ag rees w e l l w i t h t h e

r e s u l t s of t h e t h e o r e t i c a l model.

OPTICAL DETECTION OF BLOWING SNOW

The wavelength and p a r t i c l e s i z e dependence of t h e d r i f t dens i ty -ex t inc t ion

c o e f f i c i e n t r e l a t i o n s h i p sugges ts a t l e a s t two approaches t o t h e d e t e c t i o n of

blowing snow p r o p e r t i e s . One approach involves measuring t h e t r ansmi t t ance

through blowing snow wi th opto-e lec t ronic d e t e c t o r s a t two widely sepa ra t ed

wavelengths and then so lv ing f o r both t h e d r i f t d e n s i t y and 6 from t h e p a r t i c l e

s i z e d i s t r i b u t i o n . Another approach involves measuring t h e time averaged

t r a n s m i t t a n c e of an ensemble of p a r t i c l e s w i th a wide beam d e t e c t o r and count ing

i n d i v i d u a l p a r t i c l e s w i t h a narrow beam d e t e c t o r . Our o b j e c t i v e of a n inexpen-

s i v e and r e l i a b l e f i e l d component could no t be m e t by t h e f i r s t approach, as

d e t e c t o r s s e n s i t i v e t o 6-12 pm wavelengths a r e both expensive and d i f f i c u l t t o

ma in t a in i n t h e f i e l d . The second approach uses d e t e c t o r s and sources which a r e

commonly used i n t h e f i b r e - o p t i c s communications indus t ry . We chose t h e second

approach and d e t a i l i t here .

The Div i s ion of Hydrology e x t i n c t i o n meter (wide beam d e t e c t o r ) u ses a

photodiode d e t e c t o r of 1300 pm r a d i u s mounted 0.15 m from a co l l ima ted LED

source of equ iva l en t diameter . The d e t e c t o r and LED a r e s p e c t r a l l y matched,

w i t h a peak wavelength of 900 nm, t o reduce t h e r e l a t i v e i n t e n s i t y of ambient

l i g h t . The LED i s modulated t o a l l ow f u r t h e r compensation f o r ambient l i g h t

l e v e l s . The e x t i n c t i o n meter measures l i g h t i n t e n s i t y , which is r e fe renced t o

t h e una t tenuated i n t e n s i t y t o provide t h e t r ansmi t t ance and fo l lowing Eq. 3 , t h e

e x t i n c t i o n c o e f f i c i e n t . For d e t e c t o r s whose angular r a d i u s w i t h t h e p a r t i c l e is

g r e a t e r t han CL 0° , t h e e x t i n c t i o n e f f i c i e n c y must be c o r r e c t e d f o r forward

s c a t t e r i n g of l i g h t i n t o t h e d e t e c t o r . These c o r r e c t i o n s can be made by calcu-

l a t i n g forward s c a t t e r i n g i n t e n s i t i e s us ing t h e Mie theory f o r a range of angu-

lar r a d i i def ined by t h e p o s s i b l e p a r t i c l e p o s i t i o n s i n t h e beam and t h e de tec-

t o r r a d i u s . However, computat ional t imes (Wiscombe, 1980) a r e excess ive .

van d e Hu l s t (1957), Hodkinson and Greenleaves (1963) and Ungut et a l . (1981)

have shown t h a t f u l l geometr ica l o p t i c s approximations can be used f o r a c c u r a t e

l i g h t s c a t t e r i n g computations, e s p e c i a l l y when forward ang le s a r e l e s s t han 20'

and a range of wavelengths and p a r t i c l e s i z e s a r e used. These approximations

are v a l i d f o r t h e index of r e f r a c t ion , wavelength and range of p a r t i c l e s i z e s

used i n t h i s a p p l i c a t i o n .

The e x t i n c t i o n e f f i c i e n c y , Qe , as c a l c u l a t e d us ing t h e method of Nussenzveig

and Wiscombe (1980) is c o r r e c t e d f o r forward s c a t t e r i n g from Fraunhoffer d i f f r a c t i o n

and r e f r a c t i o n without i n t e r n a l r e f l e c t i o n . Pomeroy e t a 1 . (1985) have shown

t h a t forward s c a t t e r i n g from e x t e r n a l l y r e f l e c t e d l i g h t is l e s s t han 0.1% of

rece ived i n t e n s i t i e s i n blowing snow. The d i f f r a c t i o n c o r r e c t i o n AQd t o Q e

accounts f o r l i g h t d i f f r a c t e d forward by t h e p a r t i c l e i n t o a s o l i d ang le de f ined

by t h e d e t e c t o r r a d i u s Dr and d i s t a n c e R from p a r t i c l e t o d e t e c t o r . Hodkinson

and Greenleaves (1963) p re sen t a formula f o r AQ based on t h e work of van d e d

Hu l s t (1957). This formula is i n t e g r a t e d over t h e d e t e c t i o n d i s t a n c e L t o

provide a s p a t i a l l y averaged c o r r e c t i o n

where x = 27rP / A and J and J1 a r e ze ro th and f i r s t o r d e r Bessel f u n c t i o n s of r o

t h e f i r s t kind r e spec t ive ly . For t h e e x t i n c t i o n meter , t h e magnitude of AQd can

b e 50% of Q and i n c r e a s e s w i th p a r t i c l e s i z e . e

The r e f r a c t i o n c o r r e c t i o n AQ is a func t ion of t h e complex index of r e f r a c - r

t i o n m and t h e p a r t i c l e d e t e c t o r geometry. The formula presented by Hodkinson

and Greenleaves (1963) is i n t e g r a t e d over t h e d e t e c t i o n d i s t a n c e t o g ive

where A = cos8/2, B = sec48/2 , C = s in8 and 8 = arcsin(Dr/R). I n p r a c t i s e a

s i m p l i f i e d express ion can be f i t t o t h e r e s u l t s of Eq. 9 once t h e index of

r e f r a c t i o n has been s e l e c t e d . For t h e e x t i n c t i o n meter t h e magnitude of AQ is r

less than 1% of Q and is independent of p a r t i c l e s i z e . e

The e f f e c t i v e e x t i n c t i o n e f f i c i e n c y Q i s t h e Mie approximation Q cor- e f e

r e c t e d f o r forward s c a t t e r i n g and i s a func t ion of t h e d e t e c t o r geometry and t h e

r e f r a c t i v e q u a l i t i e s of t h e l i g h t d i s p e r s i v e media. Thus

Qe and Q a r e p l o t t e d a s func t ions of t h e snow p a r t i c l e r a d i u s f o r t h e e x t i n c t i o n e f

meter conf igu ra t ion i n Fig. 3. There is a dramat ic drop i n t h e e f f e c t i v e

MIE EXTINCTION EFFICIENCY

EFFECTIVE HIE EXTINCTION EFFICIENCY

1 . o L 0 20 40 80 80 100 120 140 160 180 200

SNOW PARTICLE RADIUS <mi cr. )

Figure 3. Ex t inc t ion E f f i c i e n c i e s f o r t h e Ex t inc t ion Meter. The Mie e x t i n c t i o n e f f i c i e n c y and e f f e c t i v e e x t i n c t i o n e f f i c i e n c y c o r r e c t e d f o r d i f f r a c - t i o n and r e f r a c t i o n a r e c a l c u l a t e d f o r t h e Div is ion of Hydrology Ex t inc t ion Meter .

e x t i n c t i o n e f f i c i e n c y as t h e p a r t i c l e r a d i u s i n c r e a s e s from 15 t o 50 pm. I n

terms of geometr ica l o p t i c s , f o r l a r g e r p a r t i c l e s almost a l l of t h e d i f f r a c t e d

component of s c a t t e r e d l i g h t i s s c a t t e r e d forward i n t o t h e d e t e c t o r . While t h i s

f e a t u r e reduces t h e s e n s i t i v i t y of t h e gauge, t h e e f f e c t of t h e p a r t i c l e s i z e

d i s t r i b u t i o n on t h e e x t i n c t i o n c o e f f i c i e n t w i l l be g r e a t e r t han f o r t h e v i s u a l

r ange case .

The performance of t h e e x t i n c t i o n meter can be modelled us ing Eqs. 3 , 6 , 8,

9 and 1 0 and s u b s t i t u t i n g Qef f o r Qe. The r e s u l t s a r e shown i n Fig. 4. A

v a r i a t i o n i n t h e mean snow p a r t i c l e r a d i u s through i ts normal range can r e s u l t

i n t r ansmi t t ance d i f f e r e n c e s of 0.35 f o r a cons t an t d r i f t d e n s i t y . This beha-

v i o u r n e c e s s i t a t e s t h e de t e rmin ia t ion of t h e p a r t i c l e s i z e d i s t r i b u t i o n t o

c a l i b r a t e t h e t r ansmi t t ance - d r i f t d e n s i t y r e l a t i o n s h i p . However, t h e v a r i a -

t i o n w i t h p a r t i c l e s i z e provides a t o o l f o r i n d i r e c t measurement of t h e s i z e

d i s t r i b u t i o n .

MPR.

MPR.

MPR.

100 mtor

BO micr

00 mior

40 micr

0.0- I I I 1111 1 1 1 l 1 1 1 1 I 1 1 1 1 1 1 1 I 1111 n o o o 0 . . r. Y' 2 d €i d

4 0 n

OR I F T DENS I T Y < g / m g >

Figure 4. Ex t inc t ion Meter Performance. Transmit tance c a l c u l a t e d f o r a gamma d i s t r i b u t i o n of a p r t i c l e r a d i i a of 1 0 and P of 40, 60, 80 and r 100 p.

The Divis ion of Hydrology p a r t i c l e d e t e c t o r (narrow beam d e t e c t o r ) u ses a

photodiode d e t e c t o r of 150 pm r a d i u s mounted 0.02 m from a co l l ima ted LED source

of equiva len t diameter . The peak wavelength of t ransmiss ion f o r t h i s system i s

820 nm. The p a r t i c l e d e t e c t o r counts t h e number of p a r t i c l e s per second whose

i n d i v i d u a l t r ansmi t t ances drop beyond t h e threshold l e v e l f o r d e t e c t i o n . The

t ransmi t tance , T, a s s o c i a t e d w i t h a s i n g l e p a r t i c l e i n t e r c e p t i n g a co l l imated

l i g h t beam is c a l c u l a t e d fol lowing Zuev (1970). Thus

T = T 0 - ( 1 ~ ~ 1 ~ ~ ~ 1 Qef 7 (11

where T is t h e t r ansmi t t ance antecedent t o t h e beam i n t e r c e p t i o n , I is t h e o r

i n t e r c e p t e d r a d i u s of t h e p a r t i c l e and D is t h e r a d i u s of t h e d e t e c t o r (and r

beam). The in t e rcep ted p a r t i c l e r a d i u s is t h e r a d i u s of a c i r c l e of equ iva l en t

a r e a t o t h a t area of t h e p a r t i c l e which is i n t e r c e p t e d by t h e beam. It is a

f u n c t i o n of bo th t h e p a r t i c l e r a d i u s and t h e c ros s - sec t iona l t r a j e c t o r y of t h e

p a r t i c l e through t h e beam.

The e f f e c t i v e e x t i n c t i o n e f f i c i e n c y as a f u n c t i o n of t h e i n t e r c e p t e d

p a r t i c l e r a d i u s is c a l c u l a t e d f o r t h e p a r t i c l e d e t e c t o r i n t h e same manner a s

f o r t h e e x t i n c t i o n meter. The r e s u l t s f o r t h e p a r t i c l e d e t e c t o r c o n f i g u r a t i o n

a r e p l o t t e d i n Fig. 5. Most of t h e d i f f r a c t e d l i g h t from p a r t i c l e s w i th I r

g r e a t e r t han 60 pm is s c a t t e r e d forward i n t o t h e d e t e c t o r . The e f f e c t of i n t e r -

f e r e n c e phenomena between v a r i o u s o r d e r s of s c a t t e r i n g r a y s is expressed i n t h e

incons i s t ency i n Q f o r r a d i i above 70 w. . ef

The t r ansmi t t ance a s s o c i a t e d wi th an i n t e r c e p t e d p a r t i c l e r a d i u s and t h e

v a r i a t i o n i n t h i s t r ansmi t t ance wi th a p a r t i c l e c r o s s i n g p o s i t i o n between source

and d e t e c t o r can be examined by c a l c u l a t i n g Q without i n t e g r a t i n g over d i s - ef

t a n c e from t h e d e t e c t o r (see Eqs. 8 and 9 ) . This Q (R) is h o r i z o n t a l l y spe- ef

c i f i c a s opposed t o t h e i n t e g r a t e d Q p l o t t e d i n Fig. 5. Using Eq. 11, t h e ef

t r a n s m i t t a n c e is c a l c u l a t e d a s a func t ion of I and R and t h e r e s u l t s p l o t t e d i n r

Fig. 6. The p a r t i c l e s have g r e a t e r l i g h t ex t ingu i sh ing e f f e c t s as d i s t a n c e

i n c r e a s e s from t h e d e t e c t o r . Incons i s t enc i e s i n some v a l u e s of T r e s u l t from

d i f f r a c t i o n i n t e r f e r e n c e e f f e c t s which appear more seve re when no t averaged o u t

as i n Fig. 5. These e f f e c t s a r e l e s s prominent when incoherent l i g h t and a

range of p a r t i c l e s i z e s a r e considered.

I f t h e t h re sho ld t r ansmi t t ance of d e t e c t i o n f o r t h e p a r t i c l e d e t e c t o r was

1 . 0 and t h e p a r t i c l e r a d i u s much l e s s than t h e beam r a d i u s , t hen t h e number of

snow p a r t i c l e s per u n i t volume of atmosphere N could be determined from t h e

number of p a r t i c l e s counted per second, 4 , t h e sampling a r e a of t h e beam per-

pendicular t o t h e p a r t i c l e f l u x , As, and t h e h o r i z o n t a l p a r t i c l e speed which i s

equ iva l en t t o t h e h o r i z o n t a l wind speed, u, where

N = 4/uAs . (12)

However, because t h e l i g h t beam is r e l a t i v e l y narrow, t h e sampling a r e a d i f f e r s

f o r each p a r t i c l e s i z e and i s a f u n c t i o n of t h e v e r t i c a l d e v i a t i o n of p a r t i c l e

t r a j e c t o r i e s from t h e beam c e n t r e f o r which Ir is g r e a t e r than some th re sho ld .

M I € EXTINCTION EFFICIENCY

W

W

W 1.2 - 1.1 - 1.0'-

o 20 40 60 eo 100 1 2 0 1 4 0 180 i e o 200

SNOW PARTICLE RADIUS <micr. >

Figure 5. Extinction Eff ic iencies fo r the P a r t i c l e Detector. The Mie extinc- t ion e f f ic iency and e f fec t ive ex t inc t ion eff ic iency corrected f o r d i f f r ac t i on and re f rac t ion a r e calculated fo r the Division of Hydrology P a r t i c l e Detector. .

, - - - - - - - - - - - 1 rod. 15 m i o r

- - - - - - - rod. - 40 m i o r

- - - - - - - - rod. - 70 m i o r - -

W U z < - 6

- - - - - - - - - - - I-

t. rod. - 100 m i o r

V) z < . 4 - - - - - - - - - (I: I-

.3 - - - - - - - - - - - - - - - - - - -

. I - - - - - - - m22 . 00 .01 .02 r a k - 135 m i o r 0. 0

DISTANCE FROM PARTICLE TO DETECTOR <m>

Figure 6. Single P a r t i c l e Extinction fo r the P a r t i c l e Detector. Transmittance calculated f o r s ing le pa r t i c l e s of 15, 40, 70, 100 and 135 pro radius a t various dis tances from the detector .

A complete d i s c u s s i o n of techniques f o r c a l c u l a t i n g A from t h e p a r t i c l e and S

beam geometr ies is included i n Pomeroy e t a l . (1985).

Because of background e l e c t r o n i c n o i s e l e v e l s and h igh p a r t i c l e speeds

(% 1 5 m/s) a c t u a l t h re sho ld t r ansmi t t ances of d e t e c t i o n a r e i n t r i n s i c t o i nd i -

v i d u a l d e t e c t o r s and range from 0.90 t o 0.995. A t h r e sho ld r a d i u s i s def ined as

t h e i n t e r c e p t e d r a d i u s which r e s u l t s i n a h o r i z o n t a l l y averaged t r ansmi t t ance a t

t h e th re sho ld of d e t e c t i o n . F igure 6 shows t h a t t h e e r r o r s i n u s ing t h e mean

t r ansmi t t ance become small as a t r ansmi t t ance of 1 .0 i s approached. Equation 12

i s modified t o account f o r t h i s th reshold r a d i u s by d iv id ing t h e number d e n s i t y

of p a r t i c l e s g r e a t e r than t h e th re sho ld f o r d e t e c t i o n by t h e cumulat ive f r e -

quency of p a r t i c l e s g r e a t e r than t h i s th reshold . To account f o r sampling a r e a s

s p e c i f i c t o each P t h e frequency of each P is d iv ided by t h e sampling a r e a r ' r

f o r t h a t r a d i u s . Using t h e gamma d i s t r i b u t i o n , t h e r e s u l t i n g form of t h e

equat ion i s

I n Eq. 1 3 A (P ) is t h e sampling a r e a f o r p a r t i c l e s of r a d i u s Pr and Ptr is t h e s r

p a r t i c l e r a d i u s a t t h e threshold d e t e c t i o n (when Ir = Pr) . Equation 1 3 can be

s u b s t i t u t e d i n t o Eq. 4 and wi th t h e e x t i n c t i o n c o e f f i c i e n t known from t h e ex t inc-

t i o n meter and a assumed a cons t an t , 6 can be found. With 6 known, a form of

Eq. 6 can be p r e c i s l y solved f o r t h e d r i f t dens i ty . ,

Thus t h e i n p u t s f o r t h i s blowing snow measuring system a r e a n assumed a,

t h e e x t i n c t i o n c o e f f i c i e n t from t h e e x t i n c t i o n meter, t h e number of p a r t i c l e s

counted per second by t h e p a r t i c l e d e t e c t o r and t h e mean windspeed a t t h e

h e i g h t of d e t e c t i o n . Outputs of t h e system a r e t h e d r i f t d e n s i t y of blowing

snow, t h e s i z e d i s t r i b u t i o n of snow p a r t i c l e s and t h e product nu which i s t h e

mass f l u x of blowing snow.

d

CONCLUSIONS

C a l c u l a t i o n of t h e Mie e x t i n c t i o n e f f i c i e n c i e s f o r blowing snow p a r t i c l e s

shows t h e c l a s s i c a l geometr ica l o p t i c s approximation of Qe = 2.0 i s n o t v a l i d

f o r p a r t i c l e r a d i i l e s s than 50 pm i n t h e near u l t r a v i o l e t and l e s s than 95 pm

i n t h e middle v i s i b l e range. The geometr ica l o p t i c s approximation is no t v a l i d

a t a l l f o r t h e normal range of blowing snow p a r t i c l e r a d i i when wavelengths i n

t h e nea r i n f r a r e d a r e used. S ince Q can range above 2.5 f o r p a r t i c l e r a d i i e

less than 15 u m i n v i s i b l e and near i n f r a r e d wavelengths, use of Mie approxi-

mations t o c a l c u l a t e t h e e x t i n c t i o n e f f i c i e n c y is recommended.

The v i s i b l e range - d r i f t d e n s i t y r e l a t i o n s h i p is i n v e r s e and l o g a r i t h m i c .

However, t h e r e l a t i o n s h i p i s almost l i n e a r f o r t h e range of d r i f t d e n s i t i e s from

0.01 t o 0.1 g/m3 f o r which t h e v i s i b l e range drops from approximately 15 t o 1 . 5

km. This h e l p s t o exp la in t h e low v i s i b i l i t i e s f r e q u e n t l y experienced a t "eye"

l e v e l dur ing snow storms, d e s p i t e t h e r e l a t i v e l y low d r i f t d e n s i t i e s found a t

t h e 1 .5 t o 2.5 m he igh t s . A range of wavelengths from 300 t o 2000 nm produces a

r e l a t i v e l y small change i n t h e v i s i b l e range, no wavelength possess ing c l e a r l y

s u p e r i o r l i g h t t r ansmis s ion c h a r a c t e r i s t i c s i n t h i s range. However, v a r i a t i o n

i n t h e p a r t i c l e s i z e d i s t r i b u t i o n over i ts blowing snow range produces s i g n i f i -

c a n t e f f e c t s on t h e v i s i b i l i t y w i th approximately 55% change over t h e range of

mean p a r t i c l e r a d i i . The smal le r p a r t i c l e s e x h i b i t lower v i s i b l e ranges. These

p a r t i c l e s predominate a t eye l e v e l , another f a c t o r i n low v i s i b i l i t i e s a t t h i s

he igh t .

The c o r r e c t i o n r equ i r ed t o t h e e x t i n c t i o n e f f i c i e n c y f o r forward s c a t t e r i n g

of d i f f r a c t e d l i g h t i n t o t h e d e t e c t o r s i s s i g n i f i c a n t , being approximately 50%

reduc t ion i n Q f o r l a r g e r blowing snow p a r t i c l e s . The s t r o n g v a r i a t i o n w i t h e

p a r t i c l e s i z e of t h i s c o r r e c t i o n impl ies t h a t t h e use of d e t e c t o r s w i t h r e l a -

t i v e l y wide s c a t t e r i n g acceptance ang le s can enhance t h e v a r i a t i o n of t h e

e f f e c t i v e e x t i n c t i o n e f f i c i e n c y wi th p a r t i c l e s i z e . This v a r i a t i o n permi ts t h e

use of e x t i n c t i o n meters i n p a r t i c l e s i z e de terminia t ion a s wel l a s d r i f t

dens i ty measurement.

The t h e o r e t i c a l c a l i b r a t i o n of a p a r t i c l e d e t e c t o r is complex, because

t h e sampling a r e a v a r i e s with p a r t i c l e s i z e , p a r t i c l e t r a j e c t o r i e s d iverge

from t h e beam c e n t r e r e s u l t i n g i n smaller in te rcep ted p a r t i c l e r a d i i and no

t ransmit tance l e v e l is uniquely associa ted with an in te rcep ted rad ius . The

i d e n t i f i c a t i o n of a p a r t i c l e s i z e from i ts individual t ransmit tance is there-

f o r e unl ike ly . However, when l a r g e numbers of p a r t i c l e s a r e considered, t h e

number of p a r t i c l e s g r e a t e r than some threshold can be accura te ly est imated.

This va lue wi th t h e e x t i n c t i o n c o e f f i c i e n t measured by an e x t i n c t i o n meter i s

used t o so lve f o r t h e p a r t i c l e s i z e d i s t r i b u t i o n parameters. With t h e s i z e

d i s t r i b u t i o n solved, t h e d r i f t dens i ty can be p rec i se ly ca lcu la ted . Thus t h e

o p t i c a l de tec t ion system presented here can measure both t h e quan t i ty and s i z e

of blowing snow p a r t i c l e s . These parameters a r e u s e f u l i n c a l c u l a t i n g v i s i b l e

range, t r anspor t r a t e s and sublimation r a t e s i n blowing snow.

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b

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