Observations on evaporation from snow and ice surfaces in a small wind tunnel

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NATIONAL RESEARCH C O U N C I L CANADA

D I V I S I O N O F B U I L D I N G RESEARCH

OBSERVATIONS ON EVAPORATION FROM

SNOW AND I C E S U R F A C E S I N A SMALL

WIND TUNNEL

by

G.P. W i l l i a m s

DBR I n t e r n a l R e p o r t N o .

174

O t t a w a A p r i l

1959

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PREFACE

This

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

vapour p r e s s u r e d i f f e r e n c e s , wind v e l o o i t y , s u r f a c e roughness, and changing approach c o n d i t i o n s on

e v a p o r a t i o n r a t e s were i n v e s t i g a t e d , It was found t h a t t h e g e n e r a l form of t h e e v a p o r a t i o n e q u a t i o n developed by Sverdrup was s a t i s f a a t o r y f o r t h e s e c o n t r o l l e d experiments.

T h i s s t u d y of e v a p o r a t i o n from snow and

ice

s u r f a c e s i n s i d e a wind t u n n e l i s a p r e l i m i n a r y one. I n o r d e r t o i n v e s t i g a t e t h e t h e o r y of evapora- t i o n from t h e s e s u r f a c e s , many a d d i t i o n a l experiments would be r e q u i r e d . Such a s t u d y , . i n v o l v i n g t h e

p h y a i o s of boundary l a y e r phenomena, i s beyond t h e i n s t r u m e n t a t i o n and f a c i l i t i e s a t p r e s e n t a v a i l a b l e i n t h e Snow and I o e S e c t i o n of DBR, b u t f u r t h e r work may be done i n t h e f u t u r e .

The a u t h o r of t h i s r e p o r t i s a r e s e a r o h o f f i c e r i n t h e Snow and I a e S e c t i o n . Hia s p e c i a l i n t e r e s t s i n c l u d e phenomena r e l a t i n g t o snow and i o e cover.

R.F.

Legget D i r e c t o r

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OBSERVATIONS ON EVAPORATION FROM

SNOW AND ICE SURFACES I N A SMALL WIND TUNNEL

G.P. Williams

AB STRAC T

Evaporation r a t e s from plane snow and i c e s u r f a c e s were measured under c o n t r o l l e d c o n d i t i o n s i n s i d e a c o l d room. The e f f e c t s of vapour p r e s s u r e d i f f e r e n c e s , wind v e l o c i t y , s u r f a c e roughness and changing approach c o n d i t i o n s on e v a p o r a t i o n r a t e a were i n v e s t i g a t e d . I t was found t h a t t h e Sverdrup formula

checked r e a s o n a b l y w e l l under t h e s t a b l e a i r c o n d i t i o n s encoun- t e r e d i n t h e s e experiments.

Although t h e r e have been many i n v e s t i g a t i o n s , u s i n g wind t u n n e l t e c h n i q u e s , of t h e f a c t o r s t h a t a f f e c t t h e r a t e of evapora- t i o n from a water s u r f a c e , t h e r e have been few s t u d i e s of t h e

e f f e c t of s u r f a c e roughness d u r i n g such experiments. The purpose of t h e work d e s c r i b e d i n t h i s paper i s t o determine t h e e f f e c t of s u r f a c e roughness on e v a p o r a t i o n from snow and i c e s u r f a c e s i n s i d e a wind t u n n e l . Snow and i c e s u r f a c e s have a n advantage over w a t e r s u r f a c e s i n t h a t g r a i n s i z e o r degree of roughness can be r e a d i l y determined and, f o r i c e s u r f a c e s , t h e i n v e s t i g a t i o n c a n be extended

i n t o the r e g i o n of v e r y l a r g e wind speeds w i t h o u t d i s t u r b i n g t h e s u r f a c e .

Most of t h e e a r l y work on s t u d y i n g e v a p o r a t i o n w i t h wind t u n n e l t e c h n i q u e s d i d not t a k e i n t o account t h e v a r i a t i o n of e v a p o r a t i o n r a t e s w i t h eometry, o r a t t e m p t t o a n a l y s e t h e aerodynamics of t h e problem

'i

Rohwer,

1931

,

Hinchley and Himus, 1924). Powell and G r l f f i t h s

(1936)

p o i n t e d out t h a t t h e r a t e of e v a p o r a t i o n depends on t h e dimension of t h e s u r f a c e . Powell

( 1 9 4 0 ) ~

i n one of h i s l a t e r experiments, has shown t h a t t h e r a t e of e v a p o r a t i o n c a n be i n c r e a s e d by t h e use of r i d g e s , M i l l a r

(1937)

a t t a c k e d t h e problem f r o m a more complete p h y s i c a l s t a n d p o i n t and a t t e m p t e d t o account f o r t h e e f f e c t s of i n s t a b i l i t y . He was l l m i t e d t o low wind

(5)

s p e e d s b e c a u s e , a t h i g h e r wind s p e e d s , s p r a y would come o f f t h e w a t e r s u r f a c e . Yamamoto ( 1 9 5 0 ) i n v e s t i g a t e d t h e r a t e of e v a p o r a - t i o n a t h i g h e r wind s p e e d s by u s i n g an e x p e r i m e n t a l s u r f a c e

c o n s i s t i r l g of b l o t t i n g p a p e r . P a s q u - i l l

(1943)

was ono of t h e f i r s t t o a t t e m p t t o a n a l y s e t h e aerodynamics of t h e problani and

t o p o i n t o u t some of the 1 i m i t ; a t i o n s t o t h e s t u d y o f e v a p o r a t i o n from s m a l l pans i n wind t u n n e l s . An u n p u b l i s h e d r z p o r t by Hay

(1956),

c o i n c i d i n g w i t h t h e e x p e r i r i e n t s d e s c r i b e d i n t h i s p a p e r , e x t e n d e d t h e work of P a s q u i l l t o s a t u r a t e d r o ~ g h s u r f a c e s . From a s t u d y of t h e s e p r e v i o u s i n v e . g t i g a t . i o n s i t i s apparent; t h a t any a t t e m 2 t t o r e l a t e t h e r e s u l t s o f l a b o r a t o r y s t u d i e s i n a wind t u n n e l t.o a t m o s p h e r i c c o n d i t i o n s h a s s e v e r a l l i m i t a t i o n s . A s e v a p o r a t i o n r a t e v a r i e s w i t h t h e geometry of t h e pan c o n t a i n i n g t h e evaporo t i n g m a t e r i a l , t h e r e s u l t s c a n n o t be a p p l i e d immediately t o f l e l d c o n d i t i o n s . F u r t h e r m o r e , i t i s d i f f i c u l t t o r e p r o d u c e e x a c t 1 7 i n a wind t u n n e l t h o c o n d i t i o n s a t t h e e v a p o r a t i n g s u r f a c e r e a l i z e d

i n

the f i e l d , p a r t i c u l a r l y a t m o s p h e r i c i n s t a b i l i t y and v e l o c i t y d i s t r i b u t i o n p r o f i l e ( S u t t o n ,

1953

The c h i e f a d v a n t a g e of l a b o r a t o r y i n v e s t i g a t i o n s i s t h a t v a r i a b l e s l i k e wind speed, a i r 1,empera t u r e , r e l a t i v e h w n i d i t y and s u r f a c e r o u g h n e s s c a n be c a r e f u l l y c o n t r o l l e d , Wind t u n n e l s t u d i e s a r e v a l u a b l e , t h e r e f o r e , f o r u . n d e r n t a n d i n ~ how t h e s e c o n t r o l l e d f a c t o r s i n f l u e n c e e v a p o r a t i o n and f o r e v a l u a t i n g t h e v a r i o u s e v a p o r a t i o n f o r m u l a e p r e v i o u s l y developed. EXPERIKENTAL APPARATUS

A

s m a l l c l o s e d - t y p e wind t u n n e l was b u i l t t o f i t i n s i d e

t h e cold room of t h e Snow and I c e S e c t i o n of t h e D i v i s i o n of B u i l d i n g R e s e a r c h

o old,

1956

). Viith l i m i t e d s p a c e a v a i l . a b l e , t h e t u n n e l

c o u l d n o t b e made l a r g e enough t o s i m u l a t e a t m o s p h e r i c f l o w c o n d i t i o n s . The t u n n e l was a p p r o x i m a t e l y 1 2 f t long,

4

f t h i g h , w i t h 1 - f t s q u a r e c r o s s - s e c t i o n s , and w i t h s p e c i a l vane g u i d e s b u i l t i n t o t h e elbows. The t u n n e l was t h e c l o s e d t y p e t o p e r m i t t h e a i r i n s i d e t o be of d i f f e r e n t t e m p e r a t u r e and h u m i d i t y t h a n t h e a i r i n t h e c o l d room, The t u n n e l was made i n s e c t i o n s f o r e a s y d i s m a n t l i n g o r e n l a r g e m e n t . Virith t h e s i n g l e - i n l e t , s i n g l e - w i d t h

1/3

hp f a n , i t i s p o s s i b l e t o o b t a i n mean wind s p e e d s of

60

mph i n a c r o s s - s e c t i o n a r e a of

36

s q i n . Wind speed was c o n t r o l l e d by i n s e r t i n g g r i d s i n t h e s e c t i o n n e a r t h e f a n o u t l e t ,

Two d i f f e r e n t a p p r o a c h s e c t i o n s were u s e d i n t h e l a b o r a t o r y e x p e r i m e n t s , One a p p r o a c h s e c t i o n c o n t r a c t e d from 12 by 1 2 i n . t o a c o n t r o l s e c t i o n of

6

by

6

i n . The o t h e r a p p r o a c h s e c t i o n expanded from 12 by 12 i n . t o s c o n t r o l s e c t i o n o f

6

by

36

in. Figure 1

shows a g e n e r a l scheniatic s k e t c h of t h e wind t u n n e l and e x p e r i m e n t a l a p p a r a t u s .

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WIND

_SPEED _{kEASUREh1;ENT}

Wind speeds were measured by u s i n g a

4-m

d i a m e t e r p f t o t t u b e and s p e c i a l d i f f e r e n t i a l p r e s s u r e m e t e r (Model 303-2, Decker Aviatf on Corpora t i o n ) a The p i t o t t u b e and s t a t i c p r e s s u r e t u b e

were connected t o t h e d i f f e r e n t i a l m e t e r l o c a t e d o u t s i d e t h e c o l d room. Measured mF1an w i n c l s p e e d s checked vrit;hfn

5

p e r c e n t w i t h mean wind speed measurements, usi.ng a vel-ometer.

DEW- POINT rn~~~PERATUKF:

-

m:ASTTREmNT

Dew-poin-t t e m p e r a t u r e s were measu.red by a Burton E l e c t r o n i c Dewpointer, Samples of a i r i n s i d e t h e wind t u n n e l were pumped o u t t h r o u g h t h e p i t o t - t u b e conrlections t o the Dewpointer. Because of t h e d i f f i c u l t y of measurj.ng dew p o i n t s a t low ternpera t;ure no r e a l checks on t h e a c c u r a c y o f t h e d-ew-point measurements were o b t a i n e d . However, c o n s i s t e n t r e s u l t s were o b t a i n e d , when t h e l e n s on which t h e vapour condensed vra s k e p t c l e a n . For example, if t h e a i r a t

+ 1 4 O l ? was d r i e d b y p a s s i n g over l a y e r s of cnlciunl c h l o r i d e , t h e dew- p o i n t temperat.ure could be reduced t o -2S0F: i f t h e a i r was p a r t i a l l y

s a t u r a t e d by p a s s i n g o v e r a pan of w a r r w a t e r , the dew-point tenipera- t u r e could be i n c r e a s e d t o

+8

_{and +10°3'.} _{U n t r e a t e d a i r i n the wind} t u n n e l a t a t e m p e r a t u r e of +-11_120~ had a dew-point tempera t u r e which v a r i e d between

-6

t o - € ? O F o

AIR TEMPERATURE P~'EASUFtEE'1ENT

A i r t e m p e r a t u r e s were measurod by means of a thermocouple mounted on t h e t o p of t h e p i t o t tubc. Thus, i.t; w a s e a s y when t a k i n g a v e l o c i t y p r o f i l e t o o b t a i n t e m p e r a t u r e p r o f i l e s a s w e l l . EVAPORATION RATE MEASUREME?IT

--

L i g h t aluminum t r a y s

15

cm wfde, 30 CK l o n g and 1 cm deep were f i l l e d w i t h I c e o r s c r e e n e d snow a n d p l a c e d f l u s h w i t h t h e

f l o o r of t h e t u n n e l c o n t r o l s e c t i o n . E v a p o r a t i o n r a t e s were

d e t e r m i n e d by measuring t h e weight l o s s i n t h e rnatsrj-a1 i n a known time i n t e r v a l .

PRELIMINARY EXPERIIrnNTS

I n o r d e r t o i n v e s t i g a t e t h e e f f e c t of s u r f a c e r o u g h n e s s on e v a p o r a t i o n r a t e , i t w a s f i r s t n e c e s s a r y t o d e t e r m i n e e m p i r i c a l l y t h e e f f e c t of pan s i z e , d e p t h of sample and o t h e r e x p e r i m e n t a l v a r i a b l e s on e v a p o r a t i o n r a t e . I t was a l s o n e c e s s a r y t o determine

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t h e d u r a t i o n of e x p e r i m e n t s i n o r d e r t o o b t a i n measurable e v a p o r a t i o n and t o d e c i d e w h e t h e r t h e l e n g t h of ru.n would a f f e c t t h e e v a p o r a t i o n r a t e .

F i g u r e 2 i l l u s t r a t e s some of t h e r e s u l t s from p r e l i m i n a r y e x p e r i m e n t a t i o n . F i g u r e 2 ( a ) mows t h a t e v a p o r a t i o n r a t e i n c r e a s e d o n l y s l i g h t l y w i t h t h e d u r a t i o n of e x p e r i m e n t s ; a c t u a l l y , t h e r e was o n l y a s l i g h t diffex-ence i n r a t e between e v a p o r a t i o n from a pan i n s i d e t h e wind t u n n e l f o r a n hour and a pan exposed t o t h e same c o n d i t i o n s i n s i d e t h e t u n n e l f o r 1 2 h o u r s . These r e s 1 ; l t s and

mea s u r e n ~ e n t s of dew-point tempera t u r e showed t h a t t h e r e was enough l e a k a g e of a i r from o u t s i d e t h e t u n n e l t o p r e v e n t t h e a i r i n s i d e f r o m becoming s a t u r a t e d even i f t h e e x p e r i m e n t s were r u n f o r s e v e r a l h o u r s . I t was found t h a t e x p e r i m e n t a l r u n s of from 5 0 _{t o}

60

_{m i n u t e s} r e s u l t e d i n e v a p o r a t i o n l o s s e s which c o u l d be measured w i t h t h e s c a l e s a v a i l a b l e . F i g u r e 2 ( b ) shows t h a t t h e e v a p o r a t i o n r a t e i n c r e a s e s w i t h t h e d e c r e a s i n g s i z e of e v a p o r a t i n g pan. T h i s v a r i a t i o n of e v a p o r a - t i o n r a t e w i t h t h e s i z e of pan c o n f i r m s t h e f i n d i n g s of p r e v i o u s i n v e s t i g a t o r s . F i g u r e 2 ( c ) shows t h o e f f e c t of t h e l i p of e v a p o r a t i o n pan on t h e r a t e of e v a p o r a t i o n . With f i n e - g r a i n e d snow e v a p o r a t i o n r a t e a p p e a r s t o be a f f e c t e d o n l y s l i g h t l y by d e c r e a s i n g t h e d e p t h of snow, a n d hence i n c r e a s i n g t h e l i p of . t h e pan. With a smooth i c e s u r f a c e t h e r e i s o n l y a s l i g h t d e c r e a s e i n e v a p o r a t i o n w i t h a 0.33-cm l i p . T h i s e x p e r i m e n t showed t h a t i f t h e l i p of t h e e v a p o r a t i n g pan i s n o t o v e r 0.33 cm t h e e v a p o r a t i o n r a t s w i l l n o t be a f f e c t e d .

F i g u r e 3 ( a ) shows t h e d i f f e r e n c e i n e v a p o r a t i o n r a t e s between c r u s t e d a n d u n d i s t u r b e d snow samples u n d e r s i m i l a r

c o n d i t i o n s . A h a r d c r u s t was formed by p l a c i n g t h e sample i n t h e e v a p o r a t i o n t r a y i n a warm room f o r a b o u t f i v e m i n u t e s a n d t h e n r e t u r n i n g i t t o t h e c o l d room. F i g u r e 3 ( a ) shows t h a t t h e

e v a p o r a t i o n r a t e f r o m c r u s t e d snow i s s i g n i f i c a n t l y l e s s t h a n f r o m n o n - c r u s t e d snow u n d e r s i m i l a r c o n d i t i o n s . P o s s i b l y , t h i s mathod

of c r u s t i n g t h e snow smooths t h e s u r f a c e o r impedes t h e movement of w a t e r vapour t o t h e s u r f a c e , r e s u l t i n g i n l e s s e v a p o r a t i o n .

F i g u r e 3 ( b ) shows t h a t snow s u r f a c e s w i t h o u t i n s u l a t i o n on t h e t r a y below had g r e a t e r e v a p o r a t i o n t h a n when i n s u l a t i o n was a p p l i e d . A p p a r e n t l y h e a t f l o w from t,he bottom a f f e c t e d t h e r a t e of evapora t i o n . Theref o r e , i n o r d e r t o r u n a l l e x p e r i m e n t s u n d e r s i m i l a r c o n d i t i o n s , t h e bottoms c f a l l t h e t r a y s were c o v e r e d w i t h i n s u l a t i o n .

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EFFECT OF VAPOUR PRESSURE DIFFERENCE ON EVAPORATION RATE

The f i r s t s e t of e x p e r i m e n t s was made w i t h t h e c o n t r a c t i n g approach c o n d i t i o n s and

6-

by 6-in. c o n t r o l s e c t i o n , The vapour p r e s s u r e a t

3

cm above t h e e v a p o r a t i n g s u r f a c e was o b t a i n e d by measuring t h e dew p o i n t a s d e s c r i b e d p r e v i o u s l y . The vapour p r e s s u r e a t t h e e v a p o r a t i n g s u r f a c e was o b t a i n e d by assuming t h e a i r was s a t u r a t e d a t t h e e v a p o r a t i o n s u r f a c e a t t h e t e m p e r a t u r e of t h e c o l d roam.

T h i s assumption w h i l e n o t c o m p l e t e l y v a l i d appeared t o g i v e r e a s o n a b l y c o n s i s t e n t r e s u l t s . A measurement of t h e i a e s u r f a c e t e m p e r a t u r e by means of a thermocouple imbedded i n t h e i c e i n d i c a t e d t h a t t h e t e m p e r a t u r e of t h e e v a p o r a t i n g s u r f a c e was between t h e dry- and wet-bulb t e m p e r a t u r e s .

D i f f e r e n t vapour-pressure g r a d i e n t s were o b t a i n e d by i n s e r t i n g l a y e r s of c a l c i u m c h l o r i d e o r a pan of warm w a t e r i n t o t h e upper p o r t i o n of t h e wind t u n n e l t o d r y t h e a i r o r t o add m o i s t u r e t o t h e a i r . I n t h e l a t t e r o a s e

i t

was d i f f i c u l t t o keep t h e a i r i n t h e t u n n e l a t a c o n s t a n t t e m p e r a t u r e because of t h e warming e f f e c t of t h e w a t e r ,

F i g u r e

4

i n d i c a t e s t h a t t h e r a t e of eva o r a t i o n froni i c e s u r f a c e s v a r i e s a c c o r d i n g t o D a l t o n f s Law (1802

7 .

EFFECT OF WIND VELOCITY AND SURFACE ROUGHNESS O N E V A P O R A T I O N RATE F i g u r e

5

shows t h e r e l a t i o n between e v a p o r a t i o n r a t e s and mean wind s p e e d s f o r d i f f e r e n t s u r f a c e s . The r e c o r d s were c o n s i s - t e n t showing t h a t , f o r t h i s e x p e r i m e n t a l s e t - u p a t l e a s t , t h e r a t e

of e v a p o r a t i o n was d e c i d e d l y h i g h e r from a rough s u r f a c e t h a n from a smooth s u r f a c e under s i m i l a r c o n d i t i o n s . The degree of roughness

of t h e s u r f a c e may a f f e c t t h e t u r b u l e n c e of t h e a i r o r be an i n d i c a t i o n of t h e s u r f a c e a r e a exposed which i n t u r n a f f e a t a t h e r a t e of e v a p o r a t i o n *

EFFECT OF DIFFERENT APPROACH CONDITI.0NS ON EVAPORATION RATE

A s t h e r e l a t i o n s h i p between mean wind speed, s u r f a c e t e x t u r e , and e v a p o r a t i o n r a t e may n o t h o l d f o r a l l approach c o n d i t i o n s ,

o b s e r v a t i o n s were c a r r i e d o u t u s i n g a n expanding a p p r o a c h s e c t t o n and t h e

6-

by $-inch c o n t r o l s e c t i o n . E v a p o r a t i o n r u n s were made f o r an i c e s u r f a c e and c o a r s e snow s u r f a c e only, under d i f f e r e n t c o n d i t i o n s of wind speed, I t was c o n s i d e r e d u n n e c e s s a r y t o c o n t i n u e t h e t e s t s on t h e f i n e snow s u r f a c e , a s t h e c o a r s e snow and i c e

(9)

Figure

6

shows the e f f e c t of changing t h e approach condi- t i o n s on t h e evaporation r a t e s . Apparently t h e s e c o n d i t i o n s a f f e c t t h e degree of turbulence which, i n t u r n , a f f e c t s the r a t e of

evaporation from d i f f e r e n t s u r f a c e s . The r a t e of evaporation was p l o t t e d a g a i n s t t h e l o g of the Reynold's number s o t h a t t h e r e s u l t s aould be compared t o those of o t h e r workers. The change from laminar

U

X

flow t o t u r b u l e n t flow appears t o take p l a c e a t loglO

1 =

4.9

which

Zr

a m p a r e s t o t h e value found by Yamamoto. I t i s i n t e r e & i n g t o n o t e t h a t t h e r e i s a decided d i p i n the curve i n t h i s region.

In

o t h e r words, f o r a s l i g h t l y h i g h e r wind v e l o c i t y a t t h i s p o i n t , evaporation r a t e s decreased before r a p i d l y i n c r e a s i n g a g a i n under more t u r b u l e n t

aonditions. A s S u t t o n

(1953)

p o i n t s out, a s u r f a c e which i s aerodynamically "smooth" a t low v e l o c i t i e s may become aerodynamically "roughn a s the mean v e l o c i t i e s i n c r e a s e , and between these two l i m i t s i s a t r a n s i t i o n r e g i o n i n which a s u r f a c e i s n e i t h e r smooth nor

e n t i r e l y rough.

The i n t e r e s t i n g point i s , however, t h a t with d i f f e r e n t approach c o n d i t i o n s t h e e f f e c t of s u r f a c e t e x t u r e on t h e r a t e of evaporation changed, and t h e r e l a t i o n s h i p between e v a p o r a t i o n r a t e and mean wind speed was a l t e r e d . Most previous i n v e s t i g a t o r s did n o t seem t o consider t h e e f f e o t of approach c o n d i t i o n s on t h e i r wind t u n n e l i n v e s t i g a t i o n s of evaporation l o s s e s . Probably t h i s i s one reason why the r e l a t i o n s h i p between mean wind v e l o c i t y and evapora- t i o n r a t e has shown such v a r i a b i l i t y Hiokox

(1946).

Also, f o r values

'1' l e s s than

4.9,

the evaporation r a t e s f o r coarse snow and

log10

7

i c e s a a c e s were almost t h e same under i d e n t i c a l conditions.

LABORATORY CHECK O F SVERDRUP FORMULA

Many previous i n v e s t i g a t o r s d i d n o t a o t u a l l y measure t h e v e l o c i t y p r o f i l e above the evaporating s u r f a c e and thus d i d n o t determine t h e boundary l a y e r t h i c k n e s s or t h e

ZO

a s d e f i n e d by Sverdrup

(1936).

For a l l t h e evaporating runs, a t t e m p t s were made t o measure t h e v e l o c i t y p r o f i l e a t r e g u l a r i n t e r v a l s above t h e s u r f a c e t o h e i g h t

4.5

om. The procedure was t o b r i n g t h e bottom of t h e p i t o t tube f l u s h w i t h t h e c e n t r e of t h e snow or i c e s u r f a c e and t h e n t o ' r a i s e

i t

v e r t i c a l l y i n 0.5-cm i n t e r v a l s .

With t h e smaller c r o s s - s e c t i o n and c o n t r a c t i n g approach o o n d i t i o n s t h e mean ZO was 0,002 om f o r t h e i c e s u r f a c e , 0.011 cm f o r t h e f i n e snow and 0.110 cm f o r t h e ooarse snow. With t h e measuring technique used it appeared t h a t , f o r t h e s e approach

oonditions, ZO was c o n s t a n t f o r wind speeds t e s t e d under t u r b u l e n t flow conditions. ZO was a c t u a l l y obtained by p l o t t i n g t h e v e l o c i t y p r o f i l e s on semi-log paper and extending t h e s t r a i g h t l i n e t o f i n d a t what h e i g h t above t h e s u r f a c e the v e l o c i t y was zero.

(10)

With t h e l a r g e r c r o s s - s e c t i o n and expanding approach c o n d i t i o n s t h e mean Zo was measured a s OoO029 cm f o r b o t h t h e

u

X

i c e and c o a r s e snow s u r f a c e s f o r v a l u e s of loglO

2

l e a s t h a n

ZT

5.0. For v a l u e s g r e a t e r t h a n 5.0 t h e c o a r s e snow ZO = 0.008 om and t h e i c e s u r f a c e ZO

=

0.0029 omr Some d i f f i c u l t y was e n c o u n t e r e d

i n

o b t a i n i n g good v a l u e s f o r t h i s boundary l a y e r t h i o k n e s s a t t h e lower wind v e l o c i t i e a e

The e x p e r i m e n t a l d a t a from a l l e v a p o r a t i o n experiment a

wl t h b o t h approach c o n d i t i o n s were combined and t h e Sverdrup

f _{omnula was t e s t e d (Sverdrup,}

1936).

_{F i g u r e 7 shows t h e r e l a t i o n -}

s h i p between e v a p o r a t i o n r a t e and t h e combined v a r i a b l e s of mean wind speed, vapour p r e s s u r e d i f f e r e n c e s and boundary l a y e r t h i c k n e s s .

Thus, i t seems t o give e x p e r i m e n t a l evidence t o s u p p o r t t h e e q u a t i o n developed by Sverdrup. The g e n e r a l form of t h e e q u a t i o n a p p e a r s t o be s a t i s f a c t o r y f o r t h e a d i a b a t i c c o n d i t i o n s d e s c r i b e d i n t h i s r e p o r t . The f a c t t h a t t h e c o a r s e - g r a i n e d snow e v a p o r a t i o n r a t e s f o r c o n t r a c t i n g approach c o n d i t i o n s do n o t f a l l on t h e same l i n e a s t h e o t h e r r a t e s i s p o s s i b l y due t o some t u r b u l e n c e f a c t o r which was not measured.

h

DISCUSSION OF RESULTS

T h i s p r e s e n t s t u d y of e v a p o r a t i o n from snow and i c e s u r f a c e s i s a p r e l i m i n a r y one, I n o r d e r t o a n a l y s e t h e r e s u l t s completely* a d d i t i o n a l and improved a p p a r a t u s w i l l be r e q u i r e d . A means of e v a l u a t i n g t h e t u r b u l e n c e of t h e a i r s t r e a m i s r e q u i r e d (Schubauer and Klebanoff,

1946;

Dryden 1947). A f u r t h e r check on t h e

r e l i a b i l i t y of dew-point measurements, p a r t i c u l a r l y n e a r t h e e v a p o r a t i n g s u r f a c e would be d e s i r a b l e , a s would measurement of t h e tempera t w e of t h e evapclqa t i n g s u r f a c e

.

There a r e d e f i n i t e l i m i t a t i o n s t o wind-tunnel t e c h n i q u e s f o r s t u d y i n g e v a p o r a t i o n under atmospheric c o n d i t i o n s . I t i s t h e w r i t e r ' s o p i n i o n , however, t h a t some of t h e b a s i c i d e a s of evapora- t i o n should be i n v e s t i g a t e d under c o n t r o l l e d c o n d i t i o n s b e f o r e

i n t r o d u c i n g e l l the c o m p l i c a t i o n s of s t u d y i n g e v a p o r a t i o n l o s s e s i n t h e atmosphere, Wind-tunnel s t u d i e s would be of p a r t i c u l a r u s e f o r e v a l u a t i n g t h e i n s t r u m e n t a t i o n needed f o r f i e l d o b s e r v a t i o n s . Also, t h e r e l a t i o n s h i p between s u r f a c e e v a p o r a t i o n and vapour movement t h r o u g h porous m a t e r i a l s such a s snow and g r a n u l a r s o i l s could be i n v e s t i g a t e d w i t h wind-tunnel t e c h n i q u e s . Some e x p e r i m e n t a l work on s t u d y i n g e v a p o r a t i o n from s o i l s by wind-tunnel t e c h n i q u e s h a s been done by Jensen

(1954)

i n Denmark. A s t u d y of f o r c e d -

c o n v e c t i o n h e a t t r a n s f e r from f l a t s u r f a c e s by Parmelee and Huebscher (1947) g i v e s u s e f u l i n f o r m a t i o n on t h e t y p e of a p p a r a t u s and t h e

t u r b u l e n c e measurements r e q u i r e d f o r d e t a i l e d i n v e s t i g a t i o n s of t h i s

(11)

A f t e r t h e e x p e r i m e n t s r e p o r t e d on were completed t h e w r i t e r r e c e i v e d a r e v i e w of t h e e x t e n s i v e w i n d - t u n n e l i n v e s t i g a t i o n s

conducted by Cermak and Koloseus ( 1 9 5 3 ) i n which t h e y l o o k e d i n t o t h e p o s s i b i l i t i e s of u s i n g a model t o d u p l i c a t e e v a p o r a t i o n from a n a t u r a l l a k e . T h e i r i n v e s t i g a t i o n s p r e s e n t c l e a r l y t h e problems e n c o u n t e r e d i n t r y i n g t o r e l a t e e v a p o r a t i o n e x p e r i m e n t s i n a

l a b o r a t o r y t o a t m o s p h e r i c c o n d i t i o n s ,

Because of l a c k of s p e c i f i c i n f o r m a t i o n on t h e t e m p e r a t u r e s a t which Powell ( 1 9 4 0 ) a n d Hay (1.956) c a r r i e d o u t t h e i r e x p e r i m e n t s

i t i s i m p o s s i b l e t o compare t h e p r e s e n t r o s u l t s w i t h e i t h e r of

t h e s e a u t h o r s . F o r t u n a t e l y i t was p o s s i b l e t o compare r e s u l t s w i t h d a t a from Yamamotots work (Yamamoto, 1950). F i g u r e

8

shows t h i s

comparison, u s i n g Yarnamot;ots t e r m i n o l o g y . I t f s i n t e r e s t i n g t o n o t e t h a t t h e r e s u l t s o b t a i n e d f a l l i n t o t h e same g e n e r a l p a t t e r n .

Some of t h e s c a t t e r shown i n Pig.

8

might have b e e n r e d u c e d i f a t u r b u l e n c e f a c t o r o r s u r f a c e - r o u g h n e s s t e r m h a d been i n t r o d u c e d i n t o t h e e q u a t i o n developed by Yamamoto. The e f f e c t of s u r f a c e r o u g h n e s s on e v a p o r a t i o n r a t e s o v e r open w a t e r i s s t i l l t h e s u b j e c t of some c o n t r o v e r s y ( N o r r i s ,

1948;

Montgomery, 1940). While s u r f a c e r o u g h n e s s i n t h e l a b o r a t o r y c a n n o t be compared t o s u r f a c e r o u g h n e s s u n d e r f i e l d c o n d i t i o n s where t h e a p p r o a c h c o n d i t i o n s c a n v a r y c o n s i d e r a b l y , t h e f a c t t h a t t h e S v e r d r u p e q u a t i o n c h e c k s r e a s o n a b l y w e l l 1.n t h e l a b o r a t o r y g i v e s more a u t h o r i t y t o t h i s e q u a t i o n , a t l e a s t f o r . m e a s u r i n g t h e e v a p o r a t i o n from snow and i c e s u r f a c e s u n d e r s t a b l e a i r c o n d i t i o n s .

ACKNOWLEDGMENTS

The a u t h o r i s i n d e b t e d t o M r .

J.

McNally f o r t a k i n g many of t h e measurements; t o R. Armour f o r h e l p i n i n s t r u m e n t a t i o n ; t o D r . D. S t e p h e n s c n f o r a d v i c e on c e r t a i n a s p e c t s o f t h e i n s t r u m e n t a - t i o n ; and t o

L.W.

Gold f o r encouragement, e s p e c i a l l y i n the

p r e p a r a t i o n of t h e f i n a l r e p o r t .

REFERENCES

Cermak, JOE. and

H.

J. Koloseus. Lake Hefner model s t u d i e s of wind s t r u o t u r e and e v a p o r a t i o n , R e p o r t No.

54,

JEC 20, Colorado Agric. and Mech. Coll., F o r t C o l l i n s , Colorado, November

1953.

Dalton,

J.

E x p e r i m e n t a l e s s a y s on t h e c o n s t i t u t i o n of mixed gasea; on t h e f o r c e of s t e a m o r vapour from w a t e r s and o t h e r l i q u i d s , b o t h i n a torricelllan vacuum and i n a i r ; on e v a p o r a t i o n ; and

on t h e e x p a n s i o n o f g a s e s by h e a t , Mem. Proc. I I a n c h e s t e r L i t . and P h i l . Soc., Vol.

5,

p. 535-602, 1802.

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Dryden, Hugh L. Some r e c e n t c o n t r i b u t i o n s t o t h e s t u d y of t r a n s i t i o n and t u r b u l e n t boundary l a y e r s . U.S. Nat. Adv. Corn. f o r

Aeronautics. Tech. Note no.

1168,

A p r i l

1947.

Gold, L.W. New snow and i c e r e s e a r c h l a b o r a t o r y i n Canada. J. of Glaciology, vol. 2, no.

19,

March

1956.

Hay, J.S. Evaporation from a s a t u r a t e d rough s u r f a c e i n t o a t u r b u l e n t a i r stream. A i r M i n i s t r y , a paper of t h e M e t e o r o l o g i c a l

Research Committee (London), M.R.P. no.

973,

January 24,

1956.

~ i o k o x , G.H. E v a p o r a t i o n from a f r e e w a t e r surfaoe. Trans. A.S.C.E.,

paper no. 2266, v o l e 111,

1946.

~ i n c h l e y , J.W. and G.W. Himuso E v a p o r a t i o n i n c u r r e n t s of a i r , Trans. I n a t . Chem. Engra. v o l ~ 2,

P O

57-64,

1924.

Jensen, Nartin. S h e l t e r e f f e c t

-

i n v e s t i g a t i o n s i n t o t h e aerodynamics of s h e l t e r and i t s e f f e c t s on c l i m a t e and c r o p s . The Danish T e c h n i c a l P r e s s , Copenhagen,

1954.

M i l l a r , FOG. Evaporation from f r e e w a t e r s u r f a c e s , Can. Meteor. Memoirs, vol. 1, p.

41-65,

1937.

Montgomery, ROB. Observations of v e r t i c a 1 humidity d i s t r i b u t i o n above t h e ocean s u r f a c e and t h e i r r e l a t i o n t o e v a p o r a t i o n . P a p e r s

i n

P h y s i c a l Oceanography and Moteorology (MIT and WHOI), v o l e

7,

no.

4,

19400

Norris, R. Evaporation from e x t e n s i v e s u r f a c e s of w a t e r roughened b waves. Q u a r t e r l y J o u r n a l of t h e Roy. Met. S o c i e t y , v o l e 71, no.

319,

January

1948.

Parmelee, G.V. and R.G. Huebscher. Forced c o n v e c t i o n h e a t t r a n s f e r from f l a t s u r f a c e s . Amer. Soc. of Heating and V e n t i l a t i n g Engineers, Reg. Bullo, vol.

53,

no.

3,

November

1947.

P a s q u i l l , F. Evaporation from a p l a n e , f r e e - l i q u i d s u r f a c e i n t o a

t u r b u l e n t a i r stream. Proo. Roy. Soc. of London, S e r i e s A, 182, no.

~ 9 8 8 ,

p.

75-95,

September

1943.

Powell, R.W. F u r t h e r e x p e r i m e n t s on t h e e v a p o r a t i o n of w a t e r from s a t u r a t e d s u r f a c e s . Trans, I n s t . of Chem. Engrs. vol.

18,

1940.

Powell, R.W. and

E m

G r i f f i t h s . The e v a p o r a t i o n from p l a n e and

c y l i n d r i c a l s u r f a c e s . Trans. I n s t , of Chem. Engrs. vol.

13,

P*

175-198,

1936.

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Rohwer, Carl. Evaporation from free water surfaces. U . S . Dept. Agrio. Tech. Bull. no. 271, December 19310

Sohubauer, GOB. and P o s e Klebanoff. Theory and applioation of hot- wire instrument

s

in the inve s tiga tion of turbulent boundary

layers. U.S. National Advisory Committee for Aeronautios, March 1946.

Sutton, 0 . G . _{Miorometeorology; a study of physical processes in the}

lowest layera of the earth' s atmosphere. MoGraw-Hill, New Yorko 1953, 333 Po

Sverdrup, H.U. Eddy oonductivity of the air over a amooth snow field. Geofysiske Publikaajoner, vole 11, no.

7,

p. 169, 1936 l

Yamamoto, (1. Investigation of evaporation from

cns

.

Trans. Amer. Oeophya. Union, vol. 31, no. 3,

P.

349-35 June 1950.

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ACCESS PIPES TO COLD ROOM

r

I

4 - - COLD ROOM WALLS ( INSULATED

DEW - POINTER -

No I

a

LOCATION OF

PRESSURE METER

No 2 SECTION TUNNEL EQUIPMENT IN

INTERIOR OF COLD ROOM 1 7 ' - 4 " COLD ROOM

POTENTIOMETER - . -

N a 3

PUMP FOR DEW-

No, - 7 C T I O N

No. 2 PITOT TUBE

,-PLEXIGLASS TOP

+

,,' I L ;.' THERMOCOUPLE , 7 ALUMINUM EVAPORATING .--

--

, I PAN 3 0 x 1 5 ~ 1 cm "-INSULATION FLOOR

SIDE VIEW SHOWING DETAIL OF CONTROL SECTION

(15)

10-4 3 . 0

-

.

. . . - -

,-,

COARSE SNOW 2 . 0

-

ICE 1.0- . - ~ . -~ ~- -- . OO I 2 3 4 ( 3 - 2 7 m m . SURFACE W TIME ( H R ) FIGURE 2 (a)

EFFECT ,OF DURATION OF EXPERIMENT ON RATE OF EVAPORATION

FIGURE 2 (b)

EFFECT OF AREA OF EVAPORATING SURFACE ON THE RATE OF EVAPORATION

w NO LIP LIPa3CM L I P . 6 CM (PAN FULL) (PAN 'I3 _FULL)

l-

-

2

5

_{3 . 0 -} FIGURE 2 (c) z

_a

2 c

2 . 0 u a 0

=

_{1 . 0} a. \

s

z

EFFECT OF LIP OR PAN RIM ON RATE OF

EVAPORATION INT REPORT IN

. U s 2 _{0 .} A

A

-

r l _'--_{FINE SNOW SURFACE} 'ICE SURFACE

(16)

ROOM TEMP

=

+ I 4 O F

e,-e,

=

1 - 6 5

rnb

OF

hg

x lom4 NO CRUST ON W ₄

_{.o ----}

I- SAMPLE SURFACE 4 _an

a

s

z

0

3.0

_CRUSTED _SNOW

0 ::

I- \ 2 10---.--& SAMPLE SURFACE (T: Z O

s

a

\ I . o

----

--

5 ₃

"

,

W 0 _A - - .- W

---

..-.--.--- I- O r

T

SAMPLE SURFACE 4 _an Ice a SAMPLE SURFACE

FINE SNOW COARSE SNOW

(-99

M

( -99

MM

-

3-39

MM)

FIGURE

3 ( a l

THE EFFECT OF SNOW CRUST

ON THE RATE OF

NO INSULATION

BOTTOM OF EVAPORATING

PAN ' INSULATED

0 10 16

WIND VELOCITY (FT/SEC)

5 CM ABOVE SURFACE

FIGURE

b(b)

THE EFFECT OF INSULATION ON THE BOTTOM

OF THE EVAPORATING

PAN

ON EVAPORATION

RATES

(17)

LEGEND :

ICE SURFACE FOR ALL T E S T S

ROOM T E M P t 1 4 O F

e a =

VAPOUR PRESS. OF AIR 5 CM ABOVE SURFACE

e,

=VAPOUR PRESS. AT ICE SURFACE

FIGURE

4 EFFECT OF VAPOUR

PRESSURE DIFFERENCE

(18)

LEGEND :

ROOM TEMP = + 14 O F

VAPOUR PRESS. DIFFERENCE

e,-e,

=

1 . 6 5

mb

x---X COARSE SNOW b99-3.27 MM

0-0 FINE SNOW <99 MM

a-• SMOOTH ICE SURFACE

NOTE :

EACH PLOTTED POINT REPRESENTS

AVERAGE OF 2 TESTS

MEAN WlND SPEED (FT/SEC) 3 CM ABOVE SURFACE

FIGURE

5 E F F E C T O F VARIATION

IN

WlND V E L O C I T Y

81 SURFACE ROUGHNESS ON EVAPORATION

(19)

4- 4

4.6

4.8

5.0 5.2 _5.4

LOG OF REYNOLD'S NO = log,. UI X I

a

---

CONTRACTING APPROACH EXPANDING APPROACH ROOM T E M P = + 1 4 O F VAPOUR PRESSURE DIFFERENCE = 1.55 m b

F I G U R E

6 E F F E C T OF C H A N G I N G A P P R O A C H CONDITIONS

O N T H E R A T E O F EVAPORATION.

(20)

L E G E N D : C O A q S E SNOW S U R F A C E 0 F I N E SNOW S U R F A C E I C E S U R F A C E a -HT OF M E A S U R E M E N T O F M E A N W l N D S P E E D 8 V A P O U R P R E S S U R E U a - M E A N W l N D S P E E D ea-VAPOUR P R E S S U R E O F A I R e s - S A T . V A P P R E S S . O F A I R AT S U R F A C E Zo-ROUGHNESS P A R A M E T E R

F I G U R E

7

R E L A T I O N S H I P B E T W E E N EVAPORATION

R A T E A N D T H R E E V A R I A B L E S

(21)

- - - - -- - - -.

0 MILLAR'S MEASUREMENTS

A GI-ICHI YAMAMOTO MEASURE-

MENTS WITH 2 0 C M PAN

ICE MEASUREMENT

A COARSE SbIOW MEASUREMENTS

1

(EXPANDING CROSS

-

SECTION)