Micrometeorological observations of the Snow and Ice Section, Division of Building Research, National Research Council

READ THESE TERMS AND CONDITIONS CAREFULLY BEFORE USING THIS WEBSITE. https://nrc-publications.canada.ca/eng/copyright

Vous avez des questions? Nous pouvons vous aider. Pour communiquer directement avec un auteur, consultez la première page de la revue dans laquelle son article a été publié afin de trouver ses coordonnées. Si vous n’arrivez pas à les repérer, communiquez avec nous à PublicationsArchive-ArchivesPublications@nrc-cnrc.gc.ca.

Questions? Contact the NRC Publications Archive team at

PublicationsArchive-ArchivesPublications@nrc-cnrc.gc.ca. If you wish to email the authors directly, please see the first page of the publication for their contact information.

NRC Publications Archive

Archives des publications du CNRC

This publication could be one of several versions: author’s original, accepted manuscript or the publisher’s version. / La version de cette publication peut être l’une des suivantes : la version prépublication de l’auteur, la version acceptée du manuscrit ou la version de l’éditeur.

Access and use of this website and the material on it are subject to the Terms and Conditions set forth at

Micrometeorological observations of the Snow and Ice Section,

Division of Building Research, National Research Council

Gold, L. W.

https://publications-cnrc.canada.ca/fra/droits

L’accès à ce site Web et l’utilisation de son contenu sont assujettis aux conditions présentées dans le site

LISEZ CES CONDITIONS ATTENTIVEMENT AVANT D’UTILISER CE SITE WEB.

NRC Publications Record / Notice d'Archives des publications de CNRC:

https://nrc-publications.canada.ca/eng/view/object/?id=694ee1a4-5399-48f1-a6b0-9a484e3fa748

https://publications-cnrc.canada.ca/fra/voir/objet/?id=694ee1a4-5399-48f1-a6b0-9a484e3fa748

Reprinted from P R O C E E D I N G S O F T H E F I R S T C A N A D I A N C O N F E R E N C E O N M I C R O M E T E O R O L O G Y , , P A R T

1,

Meteorological Service of Canada

Toronto, Canada,

1967.

M1CROMETE:OROLOCiICAIJ O E S E R V A T I O N S O F

THE;

SNOW

AND

I C Z S E C T I O N , D I V I S I O N O F

BUILDING

RESEARCi-I,

NATIONAL RESEARCIH G O U N C ~ I J

AESTRACT

A r e v i e w i s p r e s e n t e d o f t h e o b s e r v a t i o n s m a d e by t h e S n o w a n d I c e S e c t i o n o f t h e D i v i s i o n o f B u i l d i n g R e s e a r c h , N a t i o n a l R e s e a r c h C o u n c i l , C a n a d a , o n t h e e x c h a n g e o f h e a t a n d m o i s t u r e b e t w e e n t h e a t m o s p h e r e a n d s n o w , w a t e r a n d s o i l s u r f a c e s , a n d o n t h e g r o u n d t h e r m a l r e g i m e a n d t h e i n f l u e n c e o f s u r f a c e c h a r a c t e r i s t i c s o n t h a t r e - g i m e . I n f o r m a t i o n i s p r e s e n t e d a s w e l l o n t h e a v e r a g e s i z e o f t h e compo- n e n t s o f t h e h e a t b a l a n c e i n m i d - w i n t e r a t O t t a w a . C a n a d a , w i t h c o m m e n t s p e r t a i n i n g t o t h e d e v e l o p m e n t o f i n s t r u m e n t a t i o n .

MICROMETEOROLOGICAL OBSERVATIONS OF

THE SNOW AND ICE SECTION, DIVISION OF BUILDING RESEARCH,

NATIONAL RESEARCH COUNCIL

by

L.

W.

Gold

#at ional Research Counci

1,

Ottawa

I

l

NTRODUCT l ON

M i c r o m e t e o r o l o g i c a l s t u d i e s o f t h e Snow and I c e S e c t i o n o f t h e o f t h e D i v i s i o n o f B u i l d i n g Research o f t h e N a t i o n a l Research Council have been con-

c e r n e d with (1) t h e d e t e r m i n a t i o n o f t h c s i z e o f t h e components o f t h e h e a t and m o i s t u r e exchange a s s o c i a t e d with snow and i c e c o v e r f o r m a t i o n and a b l a t i o n , ( 2 ) t h e e v a l u a t i o n o f f i e l d t e c h n i q u e s f o r measuring t h e s e q u a n t i t i e s , and ( 3 ) t h e e s t a b l i s h m e n t o f t h e dependence o f s i g n i f i c a n t c h a r a c t e r i s t i c s o f t h e ground t h e ~ m a l regime on e a s i l y ob- s e r v e d e l e m e n t s o f t h e weather. Tne s t u d i e s h a v e n o t been concerned d i r e c t l y with t h e c l a r i f i c a t i o n o f t h e p h y s i c a l p r o c e s s e s by which h e a t and m o i s t u r e a r e exchanged bc- tween t h e atmosphere and snow, w a t e r o r ground s u r f a c e s . Most o f t h e measurements have been maue a t Ottawa f o r two p r i n c i p a l r e a s o n s :

(1) t o c a r r y o u t t h e measurements c l o s e t o a d e q u a t e s u p p o r t i n g s e r v i c e s , and ( 2 ) t o d e t e r m i n e t h e q u a n t i t i e s t h a t should b e measured f o r g i v e n f i e l d

problems and e s t a b l i s h t h e t e c h n i q r r ~ s f o r making t h e measurements.

2.

HEAT EXCHANGE AT SNOW AND GRASSED SURFACES

The f i r s t problem c o n s i d e r e d was t h a t o f d e t e r m i n i n g t h e amount o f m o i s t u r e l o s t from a snow-cover each y e a r by s u b l i m a t i o n and e v a p o r a t i o n . Observa- t i o n s a t Ottawa u s i n g s h a l l o w p a n s i n d i c a t e d t h a t t h e l o s s was about 0 . 0 2 cm i c e p e r day ( a b u t 15 cal/cm2 day) d u r i n g t h e month o f January ( 1 , 2 ). These o b s e r v a t i o n s were i n r e a s o n a b l e agreement with o b s e r v a t i o n s made by Sverdrup ( 3 ) , d e a e r v a i n ( 4 ) , and t h e C e n t r a l S i e r r a Show L a b o r a t o r y ( 5 ) , and i n d i c a t e d t h a t an e q u a t i o n o f t h e form

i s p r o b a b l y a d e q u a t e f o r p r a c t i c a l e s t i m a t e s o f s u b l i m a t i o n l o s s from snow-covers i n mid-winter. I n t h i s e q u a t i o n ,

E = r a t e o f h e a t l o s s by s u b l i m a t i o n ,

U a = a v e r a g e wind s p e e d a t h e i g h t a above t h e ground, e a = vapour p r e s s u r e i n t h e a i r a t t h e h e i g h t a ,

e = s a t u r a t i o n vapour p r e s s u r e o v e r i c e a t t h e a v e r a g e tem-

F o r E i n cal/cm2hr, U a i n cm/hr, e ,, e s i n mb, k was found t o b e about 9. 75 x 10

-'

cal/cm3mb.

C a l c u l a t i o n s o f t h e e v a p o r a t i o n l o s s d u r i n g t h e s p r i n g m e l t p e r i o d o f 1959, u s i n g t h e energy b a l a n c e e q u a t i o n and assuming Bowen's r a t i o t o b e v a l i d , i n d i c a t e d a l a r g e r v a l u e f o r k, than was o b t a i n e d by pan measurements ( 6 ) . T h i s d i f f e r e n c e may b e r e a l because t h e snow-cover o v e r wbich t h e o b s e r v a t i d n s were made was q u i t e rough, due t o t h e formation o f p e n i t e n t snow; whereas f o r t h e e v a p o r a t i o n pan o b s e r v a t i o n s , m e l t i n g o f t e n r e s u l t e d i n a s u r f a c e o f p a r t snow and p a r t water. I t

i s q u i t e p o s s i b l e , however, t h a t t h e d i f f e r e n c e was due t o o b s e r v a t i o n a l e r r o r s , p a r - t i c u l a r l y i n t h e v a l u e o f t h e n e t r a d i a t i o n , which was measured with a S c h u l z e radiom- e t e r . O b s e r v a t i o n s i n t h e s p r i n g o f 1960 gave h i g h v a l u e s f o r e v a p o r a t i o n a s well ( 7 ) . I n t h i s c a s e , t h e v a l u e used f o r n e t r a d i a t i o n was t h e mean o f t h a t measured with t h e S c h u l z e and with a Beckman and Whitley i n s t r u m e n t . The o b s e r v a t i o n s i n d i c a t e t h a t dur- i n g t h e s p r i n g m e l t p e r i o d a t Ottawa a b u t 10 and 20 p e r c e n t o f t h e w a t e r e q u i v a l e n t o f t h e snow-cover i s l o s t by e v a p o r a t i o n , and t h e r a t e o f h e a t l o s s by e v a p o r a t i o n i s about llO/cm 'day.

The d i f f i c u l t i e s e x p e r i e n c e d i n measuring n e t r a d i a t i o n l e d t o a f i e l d comparison o f two o f t h e b e t t e r n e t r a d i o m e t e r s a v a i l a b l e ; namely, a s h i e l d e d t y p e developed by t h e Commonwealth S c i e n t i f i c and I n d u s t r i a l Research O r g a n i z a t i o n o f A u s t r a l i a , and a v e n t i l a t e d Shomi t y p e made by t h e Canadian M e t e o r o l o g i c a l S e r v i c e . A random d i f f e r e n c e was o b s e r v e d between t h e a v e r a g e d a i l y v a l u e s measured by t h e two i n s t r u m e n t s t h a t was a b u t equal t o t h e a v e r a g e d a i l y n e t r a d i a t i o n being o b s e r v e d i n mid-winter ( 8 ) . C a l i b r a t i o n i n t h e long-wave l e n g t h r e g i o n c a r r i e d o u t a b u t two y e a r s l a t e r showed t h e c a l i b r a t i o n c o n s t a n t f o r t h e CSIRO i n s t r u m e n t t o be w i t h i n 1 p e r c e n t o f t h a t g i v e n by t h e m a n u f a c t u r e r . ?he c a l i b r a t i o n c o n s t a n t f o r each s i d e o f t h e Suomi t y p e i n s t r u m e n t i s dependent on t h e d e g r e e o f v e n t i l a t i o n o v e r each s u r f a c e o f t h e h e a t meter. When t h e v e n t i l a t i o n was a d j u s t e d so t h a t i t was e q u a l on both s i d e s o f t h e h e a t meter, t h e c a l i b r a t i o n c o n s t a n t was a l s o found t o b e w i t h i n 1 p e r c e n t o f t h a t s u p p l i e d by t h e manufacturer.

The o b s e r v a t i o n s on t h e h e a t and w a t e r vapour exchange a t t h e snow s u r f a c e were extended i n t o t h e summer o v e r a g r a s s e d s u r f a c e i n o r d e r t o o b t a i n an a p p r e c i a t i o n o f t h e s i z e o f t h e w i n t e r exchange r e l a t i v e t o t h a t i n slimmer. The o b s e r v a t i o n s were conducted o v e r a two-year p e r i o d . Net r a d i a t i o ! i was measured d i - r e c t l y ; h e a t flow from t h e ground was e s t i m a t e d from ground t e m p e r a t u r e observa- t i o n s : e v a p o t r a n s p i r a t i o n was e s t i m a t e d from C l a s s A pan o b s e r v a t i o n s a s well a s from o b s e r v a t i o n s on t h e wind speed and vapour p r e s s u r e d i f f e r e n c e between t h e s u r f a c e and t h e two-meter l e v e l ; and c o n v e c t i o n was determined a s t h e d i f f e r e n c e i n t h e h e a t b a l a n c e e q u a t i o n . The maximum monthly a v e r a g e n e t r a d i a t i o n was observed t o be about 280 cal/cm2day, and t h e h e a t l o s s by e v a p o t r a n s p i r a t i o n a b u t 225 c a l / c , ~ day. During a six-month p e r i o d , 1 A p r i l t o 30 September, a b o u t 48 p e r c e n t o f t h e ob- s e r v e d n e t s o l a r r a d i a t i o n was d i s s i p a t e d by e v a p o t r a n s p i r a t i o n , 42 p e r c e n t by long- wave r a d i a t i o n , 7 p e r c e n t by c o n v e c t i o n , and 3 p e r c e n t by conduction i n t o t h e ground ( 9 ) . The s u b l i m a t i o n l o s s i n mid-winter was about 10 p e r c e n t o f t h a t by evapotrans- p i r a t i o n from t h e same s i t e i n mid-summer. The o b s e r v a t i o n s i n d i c a t e t h a t , on t h e

a v e r a g e , t h e r e i s a n e t l o s s o f h e a t by r a d i a t i o n i n mid-winter, and t h a t t h e a b s o l u t e v a l u e o f t h i s l o s s i s a b u t 10 p e r c e n t o f t h e maximum monthly a v e r a g e d a i l y g a i n i n

summer. A s i t i s d i f f i c u l t t o measure e v a p a r a t i o n , e v a p o t r a n s p i r a t i o n and n e t r a d i a t i o n under f i e l d c o n d i t i o n s i n mid-summer, with an a c c u r a c y o f 10 p e r c e n t , i t a p p e a r s t h a t t h e s i z e o f t h e s e components i n mid-winter i s about t h e same a s t h e a c c u r a c y p o s s i b l e with c u r r e n t i n s t r u m e n t s and t e c h n i q u e s .

O b s e r v a t i o n s were made on t h e h e a t balance at, t h e s u r f a c e o f moss c o n t a i n e d i n t a n k s about 4 f t i n d i a m e t e r and 12 i n . deep. I t was found t h a t about 90 p e r c e n t o f t h e n e t r a d i a t i o n was d i s s i p a t e d by e v a p o r a t i o n . These o b s e r v a t i o n s , a s well a s a s s o c i a t e d o b s e r v a t i o n s made a t a bog n e a r Ottawa, were p r e s e n t e d t o t h i s sym- posium by G. P. Williams.

One o f t h e c o n c l u s i o n s o f t h e h e a t exchange s t u d i e s was t h a t i f t h e components o f t h e h e a t and water vapour b a l a n c e need t o b e measured with r e a - s o n a b l e accuracy i n mid-winter, i t will be n e c e s s a r y t o develop s u i t a b l e equipment and t e c h n i q u e s . Following a r e r e p r e s e n t a t i v e v a l u e s f o r t h e Ottawa a r e a o f t h e s i z e o f q u a n t i t i e s t o be measured and comments p e r t i n e n t t o t h e development o f i n s t r u m e n t a t i o n .

The a v e r a g e d a i l y n e t r a d i a t i v e gain t o t h e snow s u r f a c e i n t h e daytime i n mid-winter was about 30 cal/cm2, and t h e long-wave l o s s a t n i g h t about 40 cal/cm2. In o r d e r t o measure t h e s m a l l d i f f e r e n c e between t h e s e two q u a n t i t i e s with r e a s o n a b l e c o n f i d e n c e i t w i l l b e n e c e s s a r y t o p r o v e t h e r e l i a b i l i t y under f i e l d condi- t i o n s o f n e t r a d i o m e t e r s a v a i l a b l e a t p r e s e n t and, p e r h a p s , t o develop equipment with adequate accuracy. I n a d d i t i o n , c a r e f u l a n d c o n t i n u o u s c o n t r o l o f f i e l d i n s t a l l a t i o n s and f r e q u e n t checks o f t h e c a l i b r a t i o n w i l l b e r e q u i r e d p a r t i c u l a r l y f o r measurements e x t e n d i n g o v e r l o n g p e r i o d s o f time.

The vapour p r e s s u r e d i f f e r e n c e between t h e s u r f a c e and two- meter l e v e l was between 0 and 2. 5 mmHg. I t can p r o b a b l y be measured a c c u r a t e l y enough

f o r e s t i m a t e s o f s u b l i m a t i o n based on e m p i r i c a l formulae o f t h e Penman t y p e , but t h e accuracy and speed o f r e s p o n s e o f i n s t r u m e n t s a v a i l a b l e a t p r e s e n t f o r measuring water vapour d e n s i t y o r vapour p r e s s u r e impose s e v e r e limitations on t h e a p p l i c a t i o n o f a e r - odynamic o r e d d y - c o r r e l a t i o n t e c h n i q u e s f o r e s t i m a t i n g mass t r a n s f e r i n mid-winter. T h i s problem becomes more s e r i o u s t h e l o w e r t h e a i r t e m p e r a t u r e .

?he r a t e a t which h e a t was removed from t h e snow s u r f a c e by c o n v e c t i o n d u r i n g t h e daytime i n mid - w i n t e r was a b u t 3 cal/cm 2 h r , and t h e t r a n s f e r r a t e a t n i g h t t o t h e s u r f a c e was a b o u t 1. 5 cal/cm h r . F i e l d observa- t i o n s i n d i c a t e t h a t t i l e t e m p e r a t u r e g r a d i e n t i n t h e a i r a t t h e two-meter l e v e l d u r i n g t h e daytime under c l e a r sky c o n d i t i o n s was about C deg/cm and c o n s i d e r a b l y l a r g e r b u t o f o p p o s i t e s i g n a t n i g h t . Measuring t h e c o n v e c t i v e h e a t t r a n s f e r o v e r a snow s u r - f a c e u s i n g t h e aerodynamic o r e d d y - c o r r e l a t i o n t e c h n i q u e ' s h o u l d n o t be any more d i f f i - c u l t t h a n making t h e c o r r e s p o n d i n g o b s e r v a t i o n s i n summer, e x c e p t f o r t h e a d d i t i o n a l i n s t r u m e n t p r o b l a n s i n t r o d u c e d by t h e c o l d e r t e m p e r a t u r e s .

O b s e r v a t i o n s made d u r i n g January and February i n d i c a t e d t h a t d u r i n g t h e daytime t h e r a t i o between t h e c o n v e c t i v e and e v a p o r a t i v e l o s s was between 1/2 and 2/3. It w a s o b s e r v e d a l s o t h a t t h e f o l l o w i n g c o r r e l a t i o n e x i s t e d between t h e h o u r l y a v e r a g e vapour p r e s s u r e d i f f e r e n c e between t h e two-meter l e v e l . and t h e s u r f a c e ,

and t h e a s s o c i a t e d t e m p e r a t u r e d i f f e r e n c e

e a

-

e s = 1 . 0 + 0 . 2 ( T a - T s ) . ( e .and e i n mmHg, Ta and Ts i n O C)

.

T h e s e o b s e r v a t i o n s were made when t h e a v e r a g e a i r t e m p e r a t u r e was a b o u t

-

10 OC. I t would

b e e x p e c t e d t h a t t h e r a t i o between t h e c o n v e c t i v e and e v a p o r a t i v e l o s s would i n c r e a s e with d e c r e a s i n g a v e r a g e a i r t e m p e r a t u r e .

Some o b s e r v a t i o n s were made o f a l b e d o u s i n g two Q p l e y p y r h e l - i o m e t e r s mounted back t o back ( 9 ) . The monthly a v e r a g e a l b e d o o f t h e snow s u r f a c e was found t o be between 5 5 and 6 5 p e r c e n t , t h a t o f t h e g r a s s e d s u r f a c e between 10 and 20 p e r c e n t . There a p p e a r e d t o b e a tendency f o r t h e a l b e d o o f t h e g r a s s e d s u r f a c e t o i n - c r e a s e from a minimum i n s p r i n g t o a maximum i n autumn.

C o n s i d e r a t i o n was given t o t h e p o s s i b i l i t y o f a d v a n c i n g break- up o f l a k e s and r i v e r s by i n c r e a s i n g t h e a l b e d o o f t h e c o v e r t h r o u g h t h e a p p l i c a t i o n o f d u s t ( 1 0 ) . C a l c u l a t i o n s showed t h a t i t m i g h t b e p o s s i b l e t o advance break-up by

about 2 weeks i n s o u t h e r n Canada and by a b o u t 4 weeks i n t h e A r c t i c . F i e l d t r i a l s showed, however, t h a t i n much o f t h e s o u t h o f Canada t h e v a r i a b l e w e a t h e r c o n d i t i o n s t h a t e x i s t d u r i n g t h e s p r i n g thaw would a l l o w p r o b a b l y l e s s t h a n a 50 - 5 0 c h a n c e f o r d u s t i n g t o be s u c c e s s f u l .

Although p r e l i m i n a r y c a l c u l a t i o n s showed t h a t t h e s m a l l e r t h e g r a i n s i z e o f t h e d u s t t h e s n a l l e r t h e amount t h a t must be a p p l i e d t o ob- t a i n a d e q u a t e coverage, t h e f i e l d t r i a l s i n d i c a t e d t h a t economic c o n s i d e r a t i o n s make g r a i n s i z e a secondary c o n s i d e r a t i o n . The o p t i c a l p r o p e r t i e s o f t h e d u s t a p p e a r t o b e a secondary f a c t o r , a s w e l l , a s l o n g a s t h e d u s t i s d a r k . Once t h e d u s t h a s i n i t i a t e d m e l t i n g and i s submerged i n w a t e r , t h e a l b e d o o f t h e s u r f a c e i s d e t e r m i n e d p r i m a r i l y by t h e w a t e r . O b s e r v a t i o n s made a t I n u v i k s u g g e s t t h a t c l e a r i n g away t h e snow s o a s t o e x p o s e t h e i c e may be a l m o s t a s e f f e c t i v e a s d u s t i n g , from t h e p r a c t i c a l p o i n t o f view, f o r advancing m e l t i n g . I t i s c o n s i d e r e d t h a t s u f f i c i e n t s t u d y h a s now been made o f t h i s t e c h n i q u e t o a1 low a r e a l i s t i c a p p r a i s a l o f t h e a d v a n t a g e s t o b e g a i n e d t h r o u g h a p p l y i n g i t i n given a r e a s from a s t u d y o f m e t e o r o l o g i c a l r e c o r d s .

3.

GROUND T H E R M A L R E G I M E

Concurrent with t h e f o r e g o i n g o b s e r v a t i o n s on t h e h e a t and m o i s t u r e exchange a t g r a s s e d and snow s u r f a c e s , o b s e r v a t i o n s were made a t t h e same s i t e on ground t e m p e r a t u r e and t h e i n f l u e n c e o f snow-cover on h e a t flow from t h e ground. The h e a t flow from t h e ground was d i r e c t l y p r o p o r t i o n a l t o t h e d i f f e r e n c e between t h e a v e r a g e s h i e l d e d a i r t e m p e r a t u r e and t h e ground s u r f a c e t e m p e r a t u r e , and i n v e r s e l y p r o p o r t i o n a l t o t h e a v e r a g e d e p t h o f t h e snow-cover ( 1 1 ) . The o b s e r v a t i o n s showed t h a t t h e snow-cover c o u l d be assumed t o h a v e a t h e r m a l c o n d u c t i 7 r i t y e q u a l t o t h a t f o r snow o f d e n s i t y equal t o t h e a v e r a g e d e n s i t y o f t h e cover. The maximum monthly a v e r a g e h e a t f l o w from t h e ground was a b o u t 20 c a l / c m 2 d a y , and v a r i e d a p p r o x i m a t e l y s i n u s o i d a l l y t h r o u g h o u t t h e y e a r . F o r t h e t e m p e r a t u r e c o n d i t i o n s t h a t e x i s t a t Ottawa, a snow-cover 2 f t deep would n o r m a l l y a l l o w a d e p t h o f f r o s t p e n e t r a t i o n i n t o t h e ground o f l e s s

than 6 i n .

The ground t e m p e r a t u r e o b s e r v a t i o n s d e m o n s t r a t e d t h a t t h e c l a y i n which t h e measurements were made s a t i s f i e d q u i t e well t h e c o n d i t i o n s f o r s i m p l e h e a t t r a n s f e r i n a s e m i - i n f i n i t e medium f o r t e m p e r a t u r e d i s t u r b a n c e s o f p e r i o d g r e a t e r t h a n about o n e - h a l f y e a r . (12).

During t h e p e r i o d 23 December 1956 t o 3 1 March 1964, t h e annual a v e r a g e ground t e m p e r a t u r e a t t h e o b s e r v a t i o n s i t e , which was g r a s s - c o v e r e d i n summer, was between 1. 25 and 3.25 C deg warmer than t h e annual a v e r a g e a i r t e m p e r a t u r e ( 13). Snow-cover was found t o be t h e p r i n c i p a l reason f o r t h i s d i f f e r e n c e . The ground s u r - f a c e t e m p e r a t u r e u n d e r t h e snow-cover was q u i t e c o n s t a n t d u r i n g w i n t e r and between 5. 5 and 1 1 . 5 C deg warmer t h a n t h e minimum monthly a v e r a g e a i r t e m p e r a t u r e . On t h e o t h e r hand, t h e s u r f a c e t e m p e r a t u r e a t t h e b a s e o f t h e g r a s s stems was o n l y between 1 and 2 C deg wanner t h a n t h e monthly a v e r a g e a i r t e m p e r a t u r e a t t h e time o f maximum i n summer. I t was observed t h a t t h e monthly a v e r a g e s u r f a c e t e m p e r a t u r e c o r r e l a t e d well with t h e monthly a v e r a g e a i r t e m p e r a t u r e d u r i n g s p r i n g , summer and f a l l .

Ground t e m p e r a t u r e was measured under two p a r k i n g l o t s , o n e c l e a r e d o f snow i n w i n t e r , t h e o t h e r n o t , and was compared with t h o s e o b s e r v e d under. t h e g r a s s e d s i t e ( 1 4 ) . T h i s comparison d e m o n s t r a t e d n o t o n l y t h e i n f l u e n c e o f snow- cover on t h e ground thermal regime but a l s o t h e i n f l u e n c e o f t h e s i z e o f t h e c o n v e c t i v e component. The s u r f a c e o f both p a r k i n g l o t s was g r a v e l - c o v e r e d so t h a t i t was reason- a b l y well d r a i n e d and without v e g e t a t i o n . The a v e r a g e monthly s u r f a c e t e m p e r a t u r e o f t h e

t w

l o t s a t t h e t i m e o f maximum i n mid-summer was about 7 C deg warmer t h a n t h e monthly a v e r a g e a i r t e m p e r a t u r e . In mid-winter t h e p a r k i n g l o t c l e a r e d o f snow had a monthly a v e r a g e s u r f a c e t e m p e r a t u r e about equal t o t h e monthly a v e r a g e a i r t e m p e r a t u r e . I t was found t h a t t h e d i f f e r e n c e betheen monthly a v e r a g e a i r and s u r f a c e t e m ~ . ? r a t u r e s c o r r e l a t e d well d t h incoming s o l a r and n e t r a d i a t i o n . An approximate c a l c u l a t i o n i n - d i c a t e d t h a t t h e c o n v e c t i v e l o s s from t h e p a r k i n g l o t s i n summer was about 30 p e r c e n t o f t h e n e t s o l a r r a d i a t i o n , and t h e e v a p o r a t i o n l o s s 15 t o 20 p e r c e n t .

Average snow depth, a v e r a g e a i r t e n p e r a t u r e f o r given p e r i o d s , and a v e r a g e r a i n f a l l vary from o n e y e a r t o t h e n e x t and from o n e l o c a t i o n t o another. A s such f a c t o r s i n f l u e n c e t h e exchange o f h e a t and m o i s t u r e between t h e atmosphere and t h e s u r f a c e , i t would be expected t h a t f l u c t u a t i o n s i n them would i n d u c e f l u c t u a t i o n s i n t h e ground t h e r m a l regime a s well. The o b s e r v a t i o n s made a t Ottawa i n d i c a t e t h a t f l u c t u a t i o n s i n t h e annual a v e r a g e ground s u r f a c e t e m p e r a t u r e had an a m p l i t u d e o f about 1 C deg, and c o r r e l a t e d with changes from o n e y e a r t o t h e n e x t i n a v e r a g e snow depth and a i r t e m p e r a t u r e (14, 15). The amplitude o f t h e s e v a r i a t i o n s d e c r e a s e d h i t h d e p t h , but were still s i g n i f i c a n t 20 f t below t h e s u r f a c e . There was evidence o f a g r a d u a l r i s e i n t e m p e r a t u r e a t t h e 2 0 - f t depth o f about 0. 2 C deg i n 5 y e a r s . %ow-cover i n - t r o d u c e d a s i g n i f i c a n t component d t h p e r i o d o n e - h a l f y e a r i n t o t h e ground t e m p e r a t u r e wave.

4.

H E A T EXCHANGE AT WATER SURFACES

The &ow and I c e S e c t i o n h a s g i v e n a t t e n t i o n t o t h e problems o f p r e d i c t i n g d a t e s o f f r e e z e - u p and break-up, i c e growth r a t e s , maximum i c e t h i c k n e s s and formation o f f r a z i l i c e . T h i s h a s l e d t o o b s e r v a t i o n s o n t h e r a t e a t which h e a t i s

t r a n s f e r r e d between t h e atmosphere and w a t e r o r i c e s u r f a c e s .

I t was found i n t h e s t u d i e s on f r e e z e - u p t h a t t h e c o o l i n g o f a l a k e s h o u l d b e c o n s i d e r e d i n two c o n s e c u t i v e p e r i o d s ( 1 6 ) . The f i r s t i s t h e p e r i o d when t h e l a k e i s c o o l e d from t h e summer c o n d i t i o n t o t h e i s o t h e r m a l c o n d i t i o n a t 4OC. Cool- i n g d u r i n g t h i s p e r i o d i n v o l v e s m i x i n g t o t h e t h e r m o c l i n e , and c o n s e q u e n t l y t h e l a k e h a s a l a r g e "thermal i n e r t i a . " Under t h e s e c o n d i t i o n s t h e r a t e o f h e a t l o s s from t h e l a k e was d i r e c t l y p r o p o r t i o n a l t o t h e d i f f e r e n c e between t h e a v e r a g e a i r and w a t e r s u r f a c e t e m p e r a t u r e . The c o n s t a n t o f p r o p o r t i o n a l i t y depends i n p a r t on e x p o s u r e and t i m e o f y e a r , i n c r e a s i n g with d e g r e e o f exposure. O b s e r v a t i o n s on a s m a l l s h e l t e r e d l a k e i n Ottawa gave a v a l u e f o r t h e a v e r a g e h e a t t r a n s f e r c o e f f i c i e n t o f about 25 c a l / cm2dayoC (17, 18). During t h i s f a l l c o o l i n g p e r i o d , t h e e v a p o r a t i o n l o s s a p p e a r s t o b e a b o u t equal t o t h e s o l a r r a d i a t i o n a b s o r b e d by t h e water.

When t h e a v e r a g e t e m p e r a t u r e o f t h e l a k e i s lower t h a n ~ O C , o n l y t h e n e a r - s u r f a c e w a t e r i s i n v o l v e d i n t h e c o o l i n g p r o c e s s , and t h e s u r f a c e t e n - p e r a t u r e i s much more s e n s i t i v e t o changes i n weather. P r e d i c t i o n o f when i c e w i l l be- g i n t o form, t h e r e f o r e , becomes a problem o f p r e d i c t i n g weather. I f t h e t i m e f o r a given t h i c k n e s s o f i c e t o form i s used a s t h e c r i t e r i o n f o r f r e e z e - u p , t h e n i t may b e p o s s i b l e t o determine t h i s t i m e w i t h g r e a t e r c e r t a i n t y t h a n t h e t i m e t o f o r m a t i o n o f t h e f i r s t permanent i c e . I t was observed t h a t f o r t h e s m a l l s h e l t e r e d l a k e t h e t i m e t o f o r m a t i o n o f 4 t o 6 i n . o f i c e c o r r e l a t e d w e l l with t h e number o f d e g r e e

-

d a y s s i n c e t h e w a t e r was i s o t h e r m a l a t 4OC ( 1 6 ) . I t s h o u l d b e a p p r e c i a t e d t h a t t h e degree-days method i s more a method o f c o r r e l a t i o n than o f p r e d i c t i o n .

An a n a l y s i s o f a v a i l a b l e o b s e r v a t i o n s d e m o n s t r a t e d t h e very s i g n i f i c a n t i m p o r t a n c e o f such f a c t o r s a s wind, s i z e o f l a k e , and s p e e d o f c u r r e n t i n d e t e r m i n i n g when break-up w i l l o c c u r . S t u d i e s on t h e s m a l l s h e l t e r e d l a k e i n Ottawa i n d i c a t e d , a s w e l l , t h a t incoming s o l a r r a d i a t i o n must be t a k e n i n t o c o n s i d e r a t i o n when e s t i m a t i n g t h e h e a t g a i n t o t h e i c e - c o v e r d u r i n g t h i s p e r i o d ( 1 6 ) . I t was found t h a t t h e h e a t g a i n t o an i c e - c o v e r t h a t m e l t s i n p l a c e was given, a p p r o x i m a t e l y , by t h e f o l l o w i n g formula: where Qm = h e a t a v a i l a b l e f o r m e l t i n g i c e ,

2

R sw = accumulated short-wave r a d i a t i o n o v e r break-up p e r i o d ( c a l / c m 2 ) , T = accumulated d e g r e e - d a y s o v e r break-up p e r i o d O C ) . Our a b i l i t y t o p r e d i c t t h e r a t e o f h e a t and m o i s t u r e t r a n s f e r between t h e atmosphere and s u r f a c e s by c a l c u l a t i n g o r m e a s u r i n g each component o f t h e t r a n s f e r i s still i n a very i m p e r f e c t s t a t e . F o r e n g i n e e r i n g p u r p o s e s , t h e r e f o r e , i t i s p r o b a b l y more p r a c t i c a l a t t h i s t i m e t o p r e d i c t i n f o r m a t i o n , such a s p r o b a b l e r a t e o f c o o l i n g o f w a t e r b o d i e s , r a t e o f i c e growth and i c e t h i c k n e s s a t given times, from a v a i l a b l e m e t e o r o l o g i c a l and c l i m a t o l o g i c a l r e c o r d s u s i n g s t a t i s t i c a l c o r r e l a t i o n s o r e m p i r i c a l o r s e m i - m p i r i c a l formulae, a s above.

A s t u d y was u n d e r t a k e n o f a v a i l a b l e i c e t h i c k n e s s r e c o r d s t o d e t e r m i n e whether i n f o r m a t i o n o f t h i s n a t u r e c o u l d be o b t a i n e d f o r r a t e o f i c e growth. I t i n d i c a t e d t h a t t h e a v e r a g e r a t e o f growth o f i c e on l a k e s d u r i n g t h e growth p e r i o d was a b o u t f/z i n . /day and t h a t t h i s r a t e was l a r g e l y i n d e p e n d e n t o f t i m e o f y e a r o r r e - gion ( 1 9 ) . The reason f o r t h i s i s t h a t c o n d i t i o n s a t t h e t i m e o f f r e e z e - u p a r e about t h e same a t a l l l o c a t i o n s , and t h e i n c r e a s e i n h e a t l o s s t h a t w u l d b e e x p e c t e d due t o t h e d r o p i n a v e r a g e a i r t e m p e r a t u r e a s t h e w i n t e r p r o g r e s s e s i s l a r g e l y compensated f o r by t h e i n c r e a s e i n i c e t h i c k n e s s . Snow-cover i s t h e m a j o r f a c t o r t h a t i n f l u e n c e s t h e r a t e o f i c e growth and, c o n s e q u e n t l y , t h e t h i c k n e s s a t a given t i m e . S i x i n c h e s o f snow-cover r e d u c e s t h e r a t e o f growth t o 1/2 t o 1/3 t h a t f o r a snow-cover l e s s t h a n 2 i n . t h i c k . From t h e a n a l y s i s i t was p o s s i b l e t o p r e p a r e p r o b a b i l i t y c h a r t s g i v i n g r a t e o f i c e growth and i c e t h i c k n e s s t o b e e x p e c t e d a f t e r a g i v e n number o f d a y s from t h e d a t e o f freeze-up.

The i n f o r m a t i o n on i c e growth r a t e s was c o n v e r t e d t o r a t e o f h e a t l o s s i n o r d e r t o show t h e r a n g e i n t h e n e t h e a t exchange f o r Canadian l a k e s i n w i n t e r ( 2 0 ) . I t was o b s e r v e d t h a t d u r i n g t h e p e r i o d o f i c e f o r m a t i o n t h e r a t e o f n e t h e a t l o s s from t h e i c e s u r f a c e e x c e e d s 25 cal/cm2day 90 p e r c e n t o f t h e t i m e and 150 cal/cm2day 10 p e r c e n t o f t h e t i m e . The r a t e o f h e a t l o s s a p p e a r s t o d e c r e a s e grad- u a l l y w i t h i n c r e a s i n g i c e t h i c k n e s s and t o i n c r e a s e s l i g h t l y with l a t i t u d e .

5.

C O N C L U D I N G

REMARKS

I n f o r m a t i o n on t h e exchange o f h e a t and m o i s t u r e between t h e atmosphere and ground s u r f a c e i s r e q u i r e d f o r t h e development o f s a t i s f a c t o r y s o l u t i o n s f o r many e n g i n e e r i n g problems. T h i s i s p a r t i c u l a r l y t r u e where t h e problem i n y o l v e s f r e e z i n g o r thawing o f w a t e r , i n e i t h e r l a k e s o r r i v e r s o r t h e ground. I t i s o f some importance, t h e r e f o r e , t h a t we i n c r e a s e o u r knowledge o f t h e f a c t o r s t h a t c o n t r o l t h e exchange o f h e a t and m o i s t u r e a t t h e e a r t h ' s s u r f a c e , and develop i n s t r u m e n t s and t e c h - n i q u e s f o r measuring t h e s i z e o f t h e components u n d e r f i e l d c o n d i t i o n s . I t i s hoped t h a t t h e i n f o r m a t i o n d e s c r i b e d i n t h i s r e v i e w w i l l b e a u s e f u l c o n t r i b u t i o n n o t o n l y t o t h e s o l u t i o n o f e n g i n e e r i n g problems b u t a l s o t o t h e r e q u i r e d programs of i n s t r u m e n t development and o b s e r v a t i o n s on t h e p h y s i c a l p r o c e s s e s . T h i s p a p e r i s a c o n t r i b u t i o n from t h e D i v i s i o n o f B u i l d i n g Re- s e a r c h , N a t i o n a l Research C b u n c i l , and i s p u b l i s h e d w i t h t h e a p p r o v a l o f t h e D i r e c t o r o f t h e D i v i s i o n .

REFERENCES

( 1 ) Williams, G. P: 1959: Evaporation from Snow Covers i n E a s t e r n Canada, Divi- s i o n o f B u l l d i n g Research, National Research Council, NRC 5003.

( 2 ) Williams, G. P. 1961: Evaporation from Water, Snow and Ice. Proc. o f Hydro-

logy Symposium No. 2, P. 31-51, Assoc. Com. on Geodesy and Geophysics.

( 3 ) Sverdrup, H. U. 1936: The Eddy C o n d u c t i v i t y o f t h e Air Over a Smooth Snow F i e l d . Geofysislte P u b l i k a s j o n e r , 1 1 ( 7 ) .

( 4 ) d e Quervain, hl. 1952: Evaporation from t h e Snowpack. U.S. Army Corps o f Eng., T r a n s l a t i o n , Res. Note No. 8.

( 5 ) 1956: Snow Hydrology. Surmary Report o f t h e Snow I n v e s t i g a t i o n s , North Pa- c i f i c D i v i s i o n , U. S. Army Corps of L t ~ g . , P o r t l a n d . Oregon.

( 6 ) Gold. L. W. and G. P. Williams, 1961: Energy Balance During t h e Snow Melt P e r i o d a t an Ottawa S i t e . I n t . Assoc. o f Sc. Hyd., I. U. G.G., Pub. No.

54, p. 288-294.

(7) Boyd. D. W., L. W. Gold and G. P. Williams. Ra.diation Balance During t h e

Snow hlelt P e r i o d a t Ottawa, Canada. Proc. o f t h e 1961 and 1962 Annual Meeting o f t h e E a s t e r n Snow Conf. (NRC 7152).

( 8 ) Boyd, D. W. 1962: A F i e l d Comparison o f Two Types 3 f Met Radiometers. Sym- posium on t h e Heat Exchange a t Snow and I c e S u r f a c e s , Snow and I c e Sub- committee, A s s o c i a t e committee on S o i l and Snow Mechanics, 26 October 1962, TM 78.

( 9 ) Gold, L. W. and Boyd, D. W. 1965: Annual Heat and Mass T r a n s f e r a t an Ottawa S i t e . Can. J. o f E a r t h S c i . , 2 ( I ) , p. 1- 10.

(10) Williams, G. P. and Gold, L. IY. The Use of Dust t o Advance Break-up o f I c e on Lakes and R i v e r s . Proc. o f t h e 1963 Annual Meeting o f t h e E a s t e r n Snow Conf.

(11) Gold, L. W. I n f l u e n c e o f Snow Cover on Heat Flow from t h e Ground - Some ob- s e r v a t i o n s made i n t h e Ottawa a r e a . Gentbruggc 1958, Toronto General Assembly 1957, Volume IV, I n t . Assoc. o f Sc. Hydrology. I.U.G.G. ( 1 2 ) P e a r c e , D. C. and Gold, L. IV. 1959: O b s e r v a t i o n s o f Ground T e n ~ p e r a t u r e and

Heat Flcw a t Ottawa, Canada. Geophysical Research, 64 ( 9 ) ,

(13) Gold. L. W. 1963: I n f l u e n c e o f t h e Snow Cover on t h e Average Annual Ground Temperature a t Ottawa, Canada. I n t . Assoc. of S c i . Hydrology, I. U. G. G. ,

Pub. No. 61.

(14) Gold, L. \Y. I n f l u e n c e o f S u r f a c e C o n d i t i o n s on Ground Temperature. Submitted f o r p u b l i c a t i o n .

(15) Gold, L. W. 1964: A n a l y s i s o f Annual V a r i a t i o n s i n Ground Temperature a t an Ottawa S i t e . Can. J. of E a r t h S c i e n c e s , 1 ( 2 ) .

( 1 6 ) Williams, G. P. C o r r e l a t i n g Freeze-up and Break-up w i t h Weather Conditions. Submitted f o r p u b l i c a t i o n .

(17) Williams, G. P. 1963: Heat T r a n s f e r C o e f f i c i e n t s f o r N a t u r a l Water S u r f a c e s . I n t . Assoc. o f S c i . Hydrology, I . U. G.G., Pub. No. 62.

(18) Williams, G. P. 1959: Two Notes R e l a t i n g t o F r a z i l I c e Formation

-

1. An e m p i r i c a l method o f e s t i m a t i n g t o t a l h e a t l o s s e s from open

-

w a t e r s u r - f a c e s ; 2. Some o b s e r v a t i o n s on s u p e r - c o o l i n e and f r a z i l i c e production. Seminar, on I c e Problems i n Hydraulic S t r u c t u r e s . August 1959, I n t . Assoc. o f Sc. Hydrology, I. U.G.G.

(19) Williams. G. P. 1963: P r o b a b i l i t y C h a r t s f o r P r e d i c t i n g I c e Thickness.

Engineering J o u r n a l . The

(20) Williams, G. P. 1963: I c e Growth R a t e s and Heat Exchange. Symposium on Heat Exchange a t Snow and I c e S u r f a c e s , TM78. 1963, Associ'ate Committee on S o i l and Snow Mechanics, N a t i o n a l Research Council, Ottawa.