Field experiments to determine the effect of a debris layer on ablation of glacier ice

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Field experiments to determine the effect of a debris layer on ablation

of glacier ice

Nakawo, M.; Young, G. J.

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Ser

rnui

1 1 1 1

National Research

Conseil national

"la

I$

Council Canada

no.

1010

de recherches Canada

BLDG

FIELD EXPERIMENTS TO DETERMINE THE E F F E C T

O F A DEBRIS LAYER ON ABLATION O F GLACIER ICE

by

M.

Nakawo and G.

J.

Young

ANALYZED

N R . . . , r I

BLDG. RES.

Reprinted f r o m

L I B R A R Y

Annals of Glaciology

Vol.

2, 1981

82-

02-

0 2

p.

85

-

91

1

DBR P a p e r No. 1010

Division of Building R e s e a r c h

P r i c e $1.00

_OTTAWA

_{NRCC 19757}

SOMMAIRE

On a observe l'ablation d'un glacier suite

5

l'applicarion de

couches de roches dgtritiques artificielles, preparges avec

du sable d'0ttawa

(ASTM

C-1091, dont l'gpaisseur variait

de 0.01

5 0.1

m. Les donn6es recueillies sur les variables

extdrieures observges en cours drexp6rience, de msme que

l'identification positive des constantes

physiques

des

couches dgtritiques, ont permis de mettre

1

l'essai un modsle

simple propose. Les observations ont permis de constater la

justesse des predictions thEoriques. Les auteurs de cette

recherche ont voulu aller plus loin en proposant une methode

simple

q i l i

permettrait de prGdire l'ablation sous une couche

dgtritique, msme si la

cbnductivitd

ou la rgsistance

Annals of Glaciology

2

1 98 1 0 International Glaciological Society

FIELD EXPERIMENTS TO DETERMINE THE EFFECT OF

A

DEBRIS

LAYER

ON ABLATION OF GLACIER ICE

ANALYZED

M. Nakawo

(Geotechnical Section, Division of Building Research, National Research Council of Canada, Ottawa, Ontario K I A OR6, Canada)

and

G.

J. Young

(Snow and Ice Division, National Hydrology Research Institute, Inland Waters Directorate, Environment Canada, Ottawa, Ontario K I A OE7, Canada)

ABSTRACT

A b l a t i o n o f g l a c i e r i c e has been observed w i t h a r t i f i c i a l debris l a y e r s prepared w i t h Ottawa sand (ASTM C-109) ranging from 0.01 t o 0.1 m t h i c k . Data on external v a r i a b l e s observed during t h e experiments and determin- a t i o n o f physical constants o f t h e d e b r i s l a y e r s have a1 lowed the t e s t i n g o f a proposed simple model. Theoretical p r e d i c t i o n s compare

favourably w i t h the observations. Discussion

i s extended

to

a proposal f o r a simple method

by which a b l a t i o n under a d e b r i s l a y e r could be estimated even i f t h e thermal c o n d u c t i v i t y o r thermal resistance o f the m a t e r i a l were unknown.

1

.

IiqTRODUCTION

G l a c i e r t e r m i n i a r e comnonly characterized by t h e presence o f l a r g e q u a n t i t i e s o f debris, e x i s t i n g b o t h w i t h i n and on t o p o f t h e g l a c i e r i c e . The surface d e b r i s cover l a r g e l y c o n t r o l s t h e r a t e s

of

i c e m e l t which, i n turn, affects t h e mode o f formation o f g l a c i a l l y deposited land- forms. The purpose o f t h i s paper i s t o i n v e s t i - gate t h e e f f e c t o f surface d e b r i s on r a t e s o f i c e melt.

Q u a n t i t a t i v e assessment of a b l a t i o n r a t e under a d e b r i s l a y e r can a l s o be s i g n i f i c a n t f o r s t u d i e s o f g l a c i e r

mass

balance (Inoue 1977), g l a c i e r dynamics (Glazyrin 1975, Na kawo 1979), and g l a c i a l h i s t o r y (Bondarev 1961, K i t e and Reid 1977, Whalley 1979). I t i s an e s s e n t i a l f a c t o r i n any understanding o f the formation and decay of d i r t cones on g l a c i e r surfaces (Sharp

1949, Boulton 1967, Drewry 1972). I t i s pos-

s i b l e , f u r t h e m r e , t h a t i t could lead t o u s e f u l a p p l i c a t i o n of a r t i f i c i a l a b l a t i o n c o n t r o l and be adopted f o r engineerinq and h y d r o l o q i c a l purposes

r rove

and others- 1963,- W i 11 iams and Gold 1963, H i s ~ ~ c b i 1973).

The a b l a t i o n rate'under a debris l a y e r i s

a f u n c t i o n o f external v a r i a b l e s i n c l u d i n g r a d i a t i o n

and

a i r temperature, as w e l l as physical c h a r a c t e r i s t i c s o f the l a y e r such as thickness, albedo, and thermal c o n d u c t i v i t y . The e f f e c t of t h e d e b r i s l a y e r on a b l a t i o n o f g l a c i e r i c e should be studied i n a s s o c i a t i o n w i t h these variables.

Observations have been made t o evaluate the e f f e c t of a d e b r i s l a y e r on a b l a t i o n o f

g l a c i e r ice, snow, and l a k e i c e (Pstrem 1959, Wijngaarden 1961, Loomis 1970, Mbribayashi and

Higuchi 1972, Small and Clark 1974, F u j i i 1977).

These s t u d i e s suggest t h a t a very t h i n d e b r i s cover may accelerate melting, w h i l e an

increasing thickness o f d e b r i s i n h i b i t s m l t i n g . Few studies, however, have considered the e f f e c t s of

both

t h e external v a r j a b l e s and t h e physical p r o p e r t i e s o f t h e d e b r i s material. Kraus (1971 ) proposed a comprehensive theory f o r t h e a b l a t i o n under a d e b r i s layer, t a k i n g various external v a r i a b l e s i n t o consideration.

To the present authors

'

knowledge, however, t h e

theory has n o t been tested against observed data.

I n the p a s t t h e major d i f f i c u l t y i n examining t h e o r e t i c a l p r e d i c t i o n has been

lack

o f r e l i a b l e data. It i s d i f f i c u l t t o determine, i n p a r z i c u l a r , the physical p r o p e r t i e s o f d e b r i s m a t e r i a l i n the f i e l d . A r t i f i c i a l d e b r i s l a y e r s were t h e r e f o r e prepared using a known m a t e r i a l i n order t o examine the e f f e c t o f these l a y e r s on a b l a t i o n o f g l a c i e r ice. Ottawa sand (American Society f o r Testing and M a t e r i a l s C-109) was chosen as the material since many o f i t s physical p r o p e r t i e s a r e known.

2 . EXPERIMENTS

The experiments were c a r r i e d - o u t a t Peyto G l a c i e r (51' 41'N, 116' 33'W) i n t h e Rocky Mountains, Alberta, Canada, from 20 t o 22 August 1979. S i x p l o t s were prepared w i t h d r i e d Ottawa sand on r e l a t i v e l y f l a t i c e near

the

snout o f t h e g l a c i e r . They were aligned perpendicular t o t h e p r e v a i l i n g wind d i r e c t i o n and spaced

about 0.1 m apart. Each p l o t was 0.3 m square

and o f thicknesses h , given i n Table I. The

s i t e was l e v e l l e d so that, i n i t i a l l y , t h e sur- face o f each p l o t was h o r i z o n t a l .

Precautions were taken so t h a t t h e debris surface merged smoothly w i t h the surrounding i c e surfaces, b u t t h i s was n o t successful because o f l o c a l i r r e g u l a r i t i e s and general i n c l i n a t i o n (7" leeward) of the o r i g i n a l g l a c i e r surface. As t h e experiment progressed, moreover, d i f f e r - e n t i a l a b l a t i o n accentuated the i r r e g u l a r i t i e s between t h e d e b r i s surface and t h e surrounding i c e surface. A t p l o t s

E

and

F

t h e d e b r i s surface, which was o r i g i n a l l y prepared t o be

Nakmo, Young: E f f e c t o f a d e b r i s Zayer on a b l a t i o n

TABLE I. ARTIFICIAL DEBRIS LAYER AT EXPERIMENTAL SITE

SITE

Thickness, h x 10-2 m 0.86

*

0.18 1.52 1 0 . 2 3 1.92 1 0.36 3.26 1 0.30 5.16

*

0.29 10.68 1 0.37

Water content, UI = WwlWd 0.224 0.205 0.220 0.173 0.085 0.175

Surface condition wet wet wet p a r t l y d r y dry dry

Thickness o f dry l a y e r ,

hd x m

_.

2

0 1.5 0.5

Specific heat capacity Cw x J "deg" 1.45

I 1.41 1.44 1.33 1.10 1.34 Thermal

conductivity

x,,,

x

w

m'ldeg- Themal resistance R x m2 deg'l/W Dry density yd = 1 560

+

120 kg m-3

horizontal, i n c l i n e d gradually towards t h e south as a b l a t i o n proceeded. The i n c l i n a t i o n was 17" and

Y o a t

E

and

r,

r e s p e c t i v e l y , a t the end o f the experiments; no s l a n t developed a t t h e other p l o t s

.

The d r y density o f the Ottawa sand y d was

determined t o be 1 560 2 120 kg m-3 when t h e

s i t e s were prepared (evening o f 20 August). On

the morning of 21 August, however, t h e d e b r i s surface appeared t o have become saturated w i t h

water a t p l o t s

A, B,

C,

and

D.

This con-

tinued throughout the observation period and

t h e water content (w = mass o f water ww/mass o f

d r y sand Wd) f o r each p l o t was determined a t the

end o f t h e experiments (Table I). The water

seemed t o be d i s t r i b u t e d u n i f o r m l y i n the d e b r i s a t each p l o t . The d e b r i s surface was apparently

d r y a t p l o t s E and

F;

however, a wet l a y e r was

observed near the bottom o f the debris m a t e r i a l

a t both p l o t s . A d i s t i n c t boundary was found

between the d r y l a y e r near the surface and t h e

wet l a y e r near the bottom. The thickness o f

the d r y l a y e r hd as w e l l as t h e b u l k water

content u were measured a t both p l o t s (Table I ) .

A b l a t i o n d u r i n g a given p e r i o d was determined by measuring t h e increase i n t h e distance between the debris surface and a s t r i n g i n s t a l l e d h o r i z o n t a l l y over t h e s i t e a t

t h e beginning o f the experiments. For each

measurement f i v e readings were taken a t marked l o c a t i o n s w i t h i n each p l o t . The a b l a t i o n of the bare i c e beside the p l o t s was measured by the same procedure.

Atmospheric pressure p , a i r temperature

Tar and humidity were continuously recorded a t

the base camp established on a l a t e r a l moraine about 600 m from t h e s i t e . The temperature and humidity readings were c o r r e l a t e d w i t h the data, measured w i t h an Assmann v e n t i l a t e d psychrometer a t the s i t e t o take i n t o account t h e d i f f e r e n c e s between conditions a t the base camp and those a t

t h e s i t e . Incoming short-wave r a d i a t i o n was

masured w i t h

a

Sol -A-Meter (lvlatri x Inc.)

,

which

provides a read-out o f t o t a l i n t e g r a t e d i n s o l - a t i o n . Readings were taken every 1 t o 3 h

during t h e day. I n a d d i t i o n , wind speed ua,

cloud amount a,-, and c l o u d type were recorded.

3. OTTAWA SAND

Ottawa sand (ASTM C-109) i s a t y p i c a l

s i l i c a sand o f medium g r a i n size. The average

g r a i n diameter i s 0.4 mm and more than 90% by

weight f a l l s i n t o a range o f 0.2 t o 0.6 mn i n

diameter (Baker 1976). S p e c i f i c g r a v i t y and

s p e c i f i c heat o f d r y Ottawa sand a r e 2 650 kg m-3

and 0.84 J g-'deg-' r e s p e c t i v e l y (Jumikis 1977).

The s p e c i f i c heat capacity o f t h e debris l a y e r

C,

,, i s shown i n Table I.

The thermal c o n d u c t i v i t y o f O t t a w a sand Km was measured i n t e n s i v e l y by Kersten (1949) f o r a v a r i e t y o f water contents U, d r y d e n s i t i e s

Yd, and tem eratures. H i s r e s u l t s f o r Yd =

1 560 kg m-g a t 4 C are p l o t t e d against water

content u i n Figure 1. Slusarchuk and Foulger

(1973) a l s o measured c o n d u c t i v i t y a t 4 % f o r extreme cases o f water content, b u t t h e i r d r y density value was l a r g e r than t h a t obtained a t the p l o t s on the g l a c i e r . T h e i r r e s u l t s were

t h e r e f o r e corrected f o r Yd = 1 560 kg m-3 by a

r e l a t i o n between Km and Yd given by Kersten (1949) and are presented i n Figure 1.

K = 0 5I

-

SLUSARCHUK AND FOULGER 119731 ICORRECTED FOR Yd = 1.56 Mglm3! WATER SATURATION FOR 7d = 1.56 Mglm3

-

-

_... ,.,..,p

...

..-

...

.'..'' ...-

I s - 0 1 * ' J ~ t ~ ~ l 1 4 J0l~~1 n ' l m ~ ~ l l h J 1 I

I

10.' 10.' W A T E R C O N T E N T , w

Fig. 1. Thermal c o n d u c t i v i t y o f Ottawa sand f o r r d = 1 560 kg m-3 a t 4°C versus water content.

The v a r i a t i o n o f Km w i t h increase i n u i s

very small when w < 0.01. For u > 0.01, on t h e

other hand,

&

increases r a p i d l y ; the trend may

be represented by

where Km i s given by Wm-ldeg-l. This form of

r e l a t i o n between Km and u f o r r e l a t i v e l y l a r g e water contents was established by Kersten

(1949) f o r various kinds o f soi 1s.

Nakawo, Young: E f f e c t o f a d e b r i s l a y e r on a b l a t i o n

C

,

and

C

was estimated by means o f Equation (1) using t h e b u l k water content u given i n Table I. The water content i n the d r y l a y e r a t p l o t s

E

and

F

was assumed t o be 0.01, since t h e v a r i a t i o n o f Km w i t h w i s very small f o r u < 0.01. This value was used t o c a l c u l a t e t h e water content o f t h e wet l a y e r a t the two l o c a t i o n s . The value o f Km was obtained f o r each l a y e r using Equation (1). The bulk con- d u c t i v i t y f o r t h e s i t e s was then estimated using a series model o f two layers. A l l t h e estimated values f o r each p l o t are given i n Table I,

i n

which t h e thermal resistance

B ( = h/X,) f o r each l o c a t i o n i s a l s o shown. The a1 bedo o f Ottawa sand was measured l a t e r f o r wet and d r y surface conditions i n r e l a t i o n t o s o l a r a l t i t u d e . I t decreased f o r d r y (wet) conditions u n i f o r m l y (almost l i n e a r l y ) from 0.51 (0.31) t o 0.32 (0.28) as s o l a r a l t i t u d e increased from 15 t o 50 deg. t h i s range i n s o l a r a l t i t u d e being encountered d u r i n g t h e observatfon period. The r e s u l t s compared favourably w i t h those reported by B i t t n e r and S u t t e r (1935) and F r i e d r i c h (1965).

4. MODEL

The energy balance equation a t a d e b r i s surface i s given by

where 17,

F,

A, and E

are

conductive heat f l u x i n t o t h e debris, r a d i a t i o n flux, sensible heat f l u x , and l a t e n t heat f l u x , r e s p e c t i v e l y . A l l t h e terms are taken t o be p o s i t i v e downward. The energy balance equation a t the d e b r i s / i c e i n t e r f a c e i s

where M i s the heat used f o r i c e a b l a t i o n d u r i n g a u n i t period, and C ' and C" are con- d u c t i v e heat f l u x e s from the debris and towards the i c e , r e s p e c t i v e l y , again taken t o be p o s i t i v e downward. The d i f f e r e n c e between

C and C' gives t h e change i n heat stored i n the debris l a y e r . M i s given by

whew

Lf

i s t h e l a t e n t heat o f f u s i o n

(334 J

ql),

p i i s the d e n s i t y o f i c e (assumed t o be 900 kg m-3). and

r

i s t h e a b l a t i o n r a t e .

Thwe assumptions

are

made, t h a t :

C"

= 0,

which i s v a l i d f o r a temperate g l a c i e r

and i s c e r t a i n l y v a l i d f o r t h e s i t e d u r i n g August; C =

c ' ,

stored heat i n the d e b r i s l a y e r i s constant; and the temperature i n t h e d e b r i s l a y e r i s i n a s t a t i o n a r y state: a l i n e a r

p r o f i l e f o r a uniform d e b r i s l a y e r . Using these assumptions

and _{M = - T} Km _{= -} 's

h S R

where h i s the debris thickness, I$, i s the thermal c o n d u c t i v i t y , R i s the thermal resistance and Ts i s the surface teiirperature of t h e d e b r i s i n oC.

The f o l lowing expressions were assumed f o r F, H , and E (Sutton 1953, Geiger 1965, Munn 1966) :

where a i s t h e surface albedo o f the debris,

G i s the global r a d i a t i o n , A i s t h e atmospheric r a d i a t i o n , and u i s the Stephan-Boltzmann constant (5.67 x W K4);

where

B

i s t h e c o e f f i c i e n t o f

heat

t r a n s f e r (4.89

2

1.16 J rn-j deg'l cornpi l e d by Naruse

and others (1970) from the data for B obtained a t various surfaces o f g l a c i e r s , snbw f i e l d s and a r t i f i c i a l basins),

u,

i s t h e wind

speed,

and Fa

i s

t h e a i r teniperature a t t h e s i t e ; and

where L , i s

the

latent; heat o f evaporation

( 2 494 J g'l),

p

i s t h e atmospheric pressure, c i s t h e s ? e c i f i c heat capacity o f a i r (P.0 J g-ldeg-I), ea i s t h e vapour pressure i n a i r , and e, i s the vapour pressure a t

t h e

surface.

With Equations ( 4 ) t o ( 9 ) one can estimate r f o r a given R when the e x t e r n a l variables G, A, ua, Ta, p , e a , and es are given. This model i s r a t h e r more p r a c t i c a l than the one proposed by Kraus (1975), although t h e basic assumptions and the expressions a r e s i m i l a r .

5. ANALYSIS

Values o f the e x t e r n a l v a r i a b l e s f o r t h e observation period are compiled i n Table 11. Reflected r a d i a t i o n i s a f u n c t i o n o f albedo, which i s dependent on s o l a r a l t i t u d e and, accordingly, on time. T o t a l r e f l e c t e d r a d i a t i o n f o r each period was estimated by summing each reading o f global r a d i a t i o n , which had been m u l t i p l i e d by albedo a t the time o f t h e reading. Average r e f l e c t e d r a d i a t i o n i n 'Table I 1 was obtained by d i v i d i n g the t o t a l

r e f l e c t e d amount by the l e n g t h o f each period. Nominal average albedo f o r each day depends on cloud cover and o t h e r f a c t o r s because albedo i s time-dependent. The values c a l c u l a t e d f o r 21 August, however, were s i m i l a r t o those calcula- ted f o r 22 August (0.288 and 0.287 f o r wet surface on the 21st and 22nd, respectively, and 0.374 and 0.372 f o r d r y , s u r f a c e on the 21st and 22nd, r e s p e c t i v e l y ) .

Atmospheric r a d i a t i o n A was estimated by a Brunt-type empirical equation proposed by Kondo (1967)

where Ta i s i n degrees Celsius, i s i n 103Pa and C i s a parameter determined by ea, cloud amount ac, and cloud type. The estimated r e s u l t s f o r the peripds o f d a y l i g h t a r e a l s o tabulated i n Table 11. As cloud amount and type were n o t observed d u r i n g n i g h t time, A

was assumed t o be as shown i n parentheses i n Table 11.

5.1 Wet surface

W u m e d t h a t the a i r a t the debris surface was saturated a t Ts f o r a wet surface, t h a t 6 was equal t o 4.89 J r 3 d e g - l and t h a t external variables had the values given i n ' 9 Table 11. The dependence o f the a b l a t i o n r a t e

P on thermal resistance R was thus determined, using Equations (4) t o (9), by e l i m i n a t i n g

rS.

The r e s u l t s a r e shown by s o l i d l i n e s i n Figures 2 and 3. They i n d i c a t e a general asymptotic decrease o f r as R increases.

For a given R, one can a l s o estimate each f l u x component. F i s e s s e n t i a l l y a constant because IT,/<< 273 f o r a r e a l i s t i c range o f R. H and E , on the o t h e r hand, decrease from

p o s i t i v e t o negative w i t h increase i n R. For a small R ( v e r y t h i n d e b r i s l a y e r ) , Ts being close t o the i c e temperature (O°C), heat i s

Nakawo, Young: Effect of a d e b r i s l a g e r on a b l a t i o n

1

TABLE 11. EXTERNAL VARIABLES DURING OBSERVATION PERIOD

20-21 Au u s t 21 August 21-22 August (ni ghty (day ( n i g h t ) Atmospheric pressure p, 103Pa 803.1 803.1 803.1 Mean a i r temperature T,,

"C

-0.91 5.35 -0.26

Mean vapour pressure e a , 103Pa 10.17 8.17 10.56

Wind speed ua, m/s (4-5) 4-5 (4-5

Average global r a d i a t i o n G, W

m-2

0.0 525.3 0.0

Wet 0 .0 151 . O 0.0

Average r e f l e c t e d r a d i a t i o n aG, W m-2

196.4 0.0

Cloud amount a, in t e n t h s and cloud type ? 3.5 ? c i r r u s

Atmospheric r a d i a t i o n A , W m-2 (252.7) 252.7 (284.1 )

Wind speed ua, cloud amount a c , and cloud type were not observed during night time. Numerical values in parentheses were assumed f o r the estimation described i n Section 5.

transported from t h e ambient a i r t o t h e debris surface ( p o s i t i v e H and E ( c o n d e n s a t i o n ) ) , leading t o a large a b l a t i o n r a t e . For a l a r g e

R , M (and hence r ) being c l o s e t o zero owing t o t h e i n s u l a t i o n e f f e c t of t h e l a y e r , t h e energy i s almost balanced a t t h e d e b r i s surface by the t h r e e f l u x components F, H , and E.

Consequently, H and E become negative ( s e e Equation ( 5 ) ) . H = 0 when Ta =Ts and E = 0 when ea = s a t u r a t i o n vapour pressure f o r 2's.

Dotted l i n e s i n Figures 2 and 3 show t h e estimated a b l a t i o n r a t e s with upper and lower

..

! , I t 1 ! 2 0 2 1 A U G l N l G H T T I M E 1 A U N D t R D E B R I S I) B A R E I C E 2 1 A U G I D A Y T I M E )

_-

o U N D E R D E B R I S 0 B A R E I C E - W E T S U R F A C E D R Y S U R F A C E C. 5 -

*..

Fig.2. Ablation r a t e versus thermal r e s i s t a n c e f o r 20-21 August. Calculations f o r wet surface with 6 = 4.89 J W3deg-l shown by s o l i d l i n e s , 6 = 4.89

+

1.16 J V 3 d e g - l shown by dotted l i n e s ; broken l i n e shows c a l c u l - a t i o n f o r dry surface. 22 August (day 803.1 5.97 10.17 4-5 340.2 97.7 5.2 a1 tocumul us

Fig.3. Ablation r a t e versus thermal r e s i s t a n c e f o r 21-22 August. Calculations f o r wet surface with 6 = 4.89 J ~ n - ~ d e g - l shown by s o l i d l i n e s , 6 = 4.89 f 1.16 J K3deg-l shown by dotted l i n e s ; broken l i n e shows c a l c u l a t i o n f o r dry surface.

6 values of 4.89

+

1.16 J n ~ - ~ d e g - l and 4.89

-

1 .I6 J m-3deg-1, r e s p e c t i v e l y . The l a r g e r

6

value p r e d i c t s a l a r g e r a b l a t i o n r a t e . I t may be seen t h a t t h e e f f e c t of 6 value (deviation of t h e dotted l i n e s from t h e s o l i d l i n e ) decreases a s R increases f o r night time. The same tendency may be observed during t h e day, but t h e deviation becomes zero a t an i? value where H

+

E =

0.

As R increases f u r t h e r , t h e deviation becomes l a r g e r , but i n the opposite sense; t h e l a r g e r 6 value i s associated with a smaller a b l a t i o n r a t e .

Nakawo, Young: Effect of a debris l a y e r on a b l a t i o n 5.2 Dry s u r f a c e

The assumption o f s a t u r a t e d vapour pressure a t t h e surface, made f o r t h e above c a l c u l a t i o n , would be v a l i d f o r wet-surface c o n d i t i o n s ; i t would be v a l i d f o r a p p a r e n t l y d r y surfaces, as we1 1, when condensation occurs. This was t h e case d u r i n g t h e n i g h t time. I t was considered, t h e r e f o r e , t h a t t h e a b l a t i o n r a t e f o r a d r y s u r f a c e d u r i n g n i g h t t i m e was t h e same as f o r a wet surface. During t h e day time, however, i t would be reasonable t o assume f o r a d r y s u r f a c e t h a t es = ea, i.e., t h a t

E = 0.

The c a l c u l a t e d a b l a t i o n r a t e f o r a d r y s u r f a c e ( w i t h t h i s assumption) i s shown by dashed l i n e s i n Figures 2 and 3. The v a l u e o f

was taken t o be 4.89 J K 3 d e g - l i n t h e c a l c u l a t i o n s . When values o f B = 4.89

t

1.16 J ~ n - ~ d e g - l were used, t h e v a r i a t i o n i n r f o r g i v e n R was almost t h e same as f o r t h e c a l c u l a - t i o n s f o r wet surfaces.

The value o f F f o r d r y surfaces i s s m a l l e r than t h a t f o r wet surfaces because o f t h e l a r g e r albedo o f a d r y surface. The p r e d i c t e d

a b l a t i o n r a t e i s t h e r e f o r e s m a l l e r f o r d r y surfaces than f o r wet surfaces, when R i s small, where condensation occurs f o r b o t h c o n d i t i o n s . A t a l a r g e R value, however, t h e a b l a t i o n r a t e f o r d r y surfaces i s p r e d i c t e d t o be l a r g e r t h a n f o r wet surfaces. F o r l a r g e R , 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 l o s s between wet and dry surfaces i s t o o l a r g e t o be cmpensated

by the d i f f e r e n c e i n F f o r t h e two c o n d i t i o n s . 6. DISCUSSION

Observed a b l a t i o n r a t e s a t t h e s i t e a r e p l o t t e d i n F i g u r e s 2 and 3 u s i n g s o l i d c i r c l e s f o r t h e n i g h t - t i m e observations and open c i r c l e s f o r day. A b l a t i o n r a t e s o f bare i c e beside t h e p l o t s a r e a l s o shown w i t h s o l i d ( n i g h t t i m e ) and open (day time) arrows as reference. The bare i c e s u r f a c e was d i r t y and i t s albedo observed t o be 0.32 f 0.02 near noon when s o l a r a l t i t u d e was about 50".

The p r e d i c t e d a b l a t i o n r a t e compared reasonably w e l l w i t h t h e observed r e s u l t s . (Note t h a t r e s u l t s a t p l o t s

E

and

F

d u r i n g day t i m e a r e t o be compared w i t h t h e broken l i n e s , n o t w i t h t h e s o l i d l i n e s . )

For small R values a l a r g e r a b l a t i o n r a t e than p r e d i c t e d was observed a t p l o t s

A,

B

,

and

C

d u r i n g day time, suggesting t h a t t h e a c t u a l v a l u e o f 6 could be s l i g h t l y l a r g e r than the v a l u e used f o r t h e c a l c u l a t i o n s . This i s reasonable s i n c e s u r f a c e roughness i s g r e a t e r a t t h e s i t e t h a n a t t h e n a t u r a l s u r f a c e owing t o t h e presence o f t h e p l o t s . The pre- d i c t e d values f o r p l o t s

E

and

F

d u r i n g day t i m e on 22 August a r e a l s o s m a l l e r t h a n t h e observed a b l a t i o n r a t e . T h i s discrepancy i s probably caused by an i n c r e a s e i n i n c l i n a t i o n o f t h e d e b r i s s u r f a c e towards t h e south, as mentioned i n s e c t i o n 2.

The general agreement between t h e pre- d i c t e d and observed r e s u l t s suggests t h a t one can p r e d i c t a b l a t i o n i f t h e e x t e r n a l v a r i a b l e s and thermal r e s i s t a n c e o f t h e d e b r i s l a y e r are known. Determination o f thermal r e s i s t a n c e , however, i s a most d i f f i c u l t problem f o r an unknown d e b r i s m a t e r i a l i n t h e f i e l d .

The model described i n s e c t i o n 4 c o u l d a l s o be used t o p r e d i c t s u r f a c e temperature

T, by e l i m i n a t i n g M from Equations ( 5 ) and (6). E s t i m a t i o n was made u s i n g t h e data f o r e x t e r n a l v a r i a b l e s o b t a i n e d between 11.15 and 13.45 h l o c a l t i m e on 21 August. The p r e d i c t e d s u r f a c e temperature i s shown i n F i g u r e 4a w i t h s o l i d (wet surface) and broken ( d r y s u r f a c e ) l i n e s . The a b l a t i o n r a t e was a l s o estimated f o r t h i s

C B A R E I C I -

-

W f T S U R F A C E

--- -

D R Y SURFhCf

_-

Fig.4. Surface temperature ( a ) and a b l a t i o n r a t e (b) versus thermal r e s i s t a n c e from 11.15 t o 13.45 h l o c a l time, 21 August; s u r f a c e temperature measured a t 12.40 h l o c a l time. C a l c u l a t i o n s f o r wet s u r f a c e w i t h

6 = 4.89 J ~ n - ~ d e g - l shown w i t h s o l i d l i n e s ; c a l c u l a t i o n s f o r d r y s u r f a c e w i t h

6 = 4.89 J m-3deg-1 shown w i t h broken l i n e s ; c a l c u l a t i o n s f o r b o t h wet and d r y surfaces w i t h 6 = 4.89

2

1 . I 6 J r 3 d e g - l shown by d o t t e d l i n e s . r a t h e r s h o r t p e r i o d by means o f t h e same procedure ( F i g . 4b). Observed a b l a t i o n r a t e s d u r i n g t h i s p e r i o d and s u r f a c e temperature measured a t 12.40 h l o c a l t i m e a r e a l s o p l o t t e d f o r comparison. The estimated and observed values agree f a v o u r a b l y f o r b o t h s u r f a c e temperature and a b l a t i o n r a t e . I t should be p o s s i b l e , t h e r e f o r e , t o e s t i m a t e thermal r e s i s t a n c e from s u r f a c e temperature measurements u s i n g Equations ( 5 ) t o (9).

I

I 10 100

THERMAL RESISTANCE ITABLE II. 10.' rn2 "ClW

Fig.5. Comparison o f thermal r e s i s t a n c e s a t s i t e s estimated from s u r f a c e temperature w i t h values obtained f r a n t h e p h y s i c a l constants o f Ottawa sand. E s t i m a t i o n s made from a b l a t i o n r a t e (open c i r c l e s ) and e x t e r n a l parameters ( s o l i d c i r c l e s )

.

Nakawo, Young: E f f e c t o f a d e b r i s l a y e r on a b l a t i o n

The e s t i m a t e s were made u s i n g o b s e r v a t i o n s

f o r t h e noon p e r i o d on 21 August. Estimated

thermal r e s i s t a n c e i s compared i n F i g u r e 5 ( s o l i d c i r c l e s ) w i t h t h e r e s i s t a n c e g i v e n i n Table I. Thermal r e s i s t a n c e was o b t a i n e d a l s o from t h e d a t a on s u r f a c e temperature and a b l a t i o n r a t e u s i n g Equations ( 4 ) and ( 6 ) , b u t t h i s method i s n o t o f p r a c t i c a l i n t e r e s t because a b l a t i o n r a t e i s n o t u s u a l l y known and

i s t h e term t o be determined. Values o b t a i n e d

by t h i s method a r e a l s o compared i n F i g u r e 5 (open c i r c l e s ) w i t h t h e values g i v e n i n Table I. Thermal r e s i s t a n c e s o b t a i n e d by t h e t h r e e d i f f e r e n t methods compare reasonably w e l l w i t h each o t h e r .

I t i s f a i r l y easy t o determine t h e s u r f a c e temperature o f a d e b r i s l a y e r o v e r a wide area

by means o f remote sensing. One can estimate,

t h e r e f o r e , t h e thermal r e s i s t a n c e and consequen- t l y t h e a b l a t i o n r a t e under t h e d e b r i s l a y e r f r o m a knowledge o f e x t e r n a l v a r i a b l e s o n l y .

The model now proposed n e g l e c t s t h e change

o f s t o r e d h e a t i n a d e b r i s l a y e r , a l t h o u g h i t c o u l d be s i g n i f i c a n t f o r a t h i c k l a y e r w i t h a l a r g e h e a t c a p a c i t y . N e i t h e r i s t h e e f f e c t o f r a i n f a l l i n c l u d e d . S i g n i f i c a n t h e a t c o u l d be t r a n s p o r t e d by water p e r c o l a t i o n i n t o a porous, t h i c k d e b r i s l a y e r (Yoshida, unpublished)

.

F o r a v e r y t h i n , o r s c a t t e r e d , d e b r i s l a y e r on a g l a c i e r surface, albedo must be considered as a v a r i a b l e . Such a s i t u a t i o n i s o u t s i d e t h e scope o f t h e p r e s e n t paper, b u t i t i s an i m p o r t a n t c o n s i d e r a t i o n s i n c e a c c e l e r a t e d a b l a t i o n takes p l a c e when t h i s c o n d i t i o n p r e v a i 1s (Megahan and o t h e r s , 1970, Higuchi

and Nagoshi 1975. F u r t h e r s t u d y w i l l be

necessary on t h i s s u b j e c t . ACKNOWLEDGEMENTS

The a u t h o r s a r e g r a t e f u l f o r t h e a s s i s - tance g i v e n i n t h e f i e l d by N. Maeno and H. N a r i t a o f t h e I n s t i t u t e o f Low Temperature Science, Hokkaido, Japan, and a r e i n d e b t e d t o L.W. Gold o f t h e D i v i s i o n o f B u i l d i n g Research, N a t i o n a l Research Council o f Canada, f o r r e v i e w i n g t h e manuscript.

T h i s paper 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 Research, N a t i o n a l Research Council o f Canada, and i s p u b l i s h e d w i t h t h e approval 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 .

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