SL;\TER--STUDIES ON THE KNOSE CLACILR, 1927 385

STUDIES ON T H E RHONE GLACIER, 1927 THE RELATIONSHIP BETWEEN THE AVERAGE AIR

TEMPERATURE AND THE RATE O F MELTING OF THE SURFACE OF THE GLACIER

By GEORGE SLATER, D.Sc., D.I.C., A.R.C.S.

(Cominunicated by Sir GILBERT WALKER, C.S.I., F.K.S.)

[Manuscript received March 9-Reud June 19, 11!2!l.1

I .-IXTRODUCTIOS. Observations in Spitsbergen in the summer of 1921 suggested

to the author a simple tentative relationship between the average air temperature and the rate of melting of the Nordenskiold Glacier [s]'. This relationship may be expressed as A f = + (t -32 F.) where .If=thickness (in feet) of ice melted per month (30 days), and t=average monthly temperature (in OF.). In other words, .z inches of ice were melted per day for each degree (F.) above the freezing point, undcr normal atmospheric conditions, wind and rsin producing deviations from the normal.

This relationship was supported by observations of the rate of retreat of the glacier during the previous 10 years coupled with the records of temperatures for the same period determined a t the Green Harbour Meteorological Station. The relationship was again strikingly supported two years later, the retreat of the ice on this occasion being measured by Dr. Longstaff, and the records of tem- perature determined from daily records at the Meteorological Office at South Kensington.

With the object of further testing the truth of this tentative law, observations were conducted on the Rhone Glacier 1927, over a period of twenty days.

PREVIOUS OBSERVATIONS OS THE t\Br.n.rIoX OF GLACIERS. Even on empirical grounds the melting of a glacier is a

meteorological question. The rate of melting varies with the seasons, and is greatest towards the end of the summer months. Forbes [I], for example, in 1842 noted that the surface of a glacier wns lowcrecl 70 feet in a few months of a very hot summer, and he attributes thi's abnormal rate to the efects of direct solar heat, contact of warm air, and the washing of rain.

Nevertheless, in spite of the amount of work which has since been accomplished on the ablation of glaciers in Arctic, Norwegian and Alpine areas, only indirect correlations with the climatic factor have been attempted. These correlations fall under two headings- (I) altitude, and ( 2 ) latitude.

( I ) Altitude .-Metcanton shows in a table the relationship between the rate of melting of the Rhone Glacier and altitude [4]. He therefore came to the following conclusion :-

1 Numbers in square brackets refer to the bibliography at the end.

386 SLATER-STUDIIJS ON THE RHOXE GLACIER, 1927

" L'ablation dCcroit quand I'altitude croft ; son dCcroisse- ment n'est pas proportionnel A I'accroissemcnt de l'altitude, mais est plus lent."

The almost entire absence of records of temperature for the area of the Rhone Glacier is a regrettable omission of the valuable memoir on this classical glacier.

(2) Lotitude.-The relationship between ablation of ice a t 400 m. below the snow line and latitude has been demonstrated in tables by Hess. A revised table by Hoe1 [3] is as follows:-

I. Spitsbergen 79" 01 N., annual rate of ablation = 1.4 m. 2. Greenland 70" 3d N., annual rate of ablation = 2.2 m. 3. Scandinavia 67" 201 N., annual rate of ablation = 2.5-3.0 m.

4. The Alps 40" d N., annual rate of ablation = 4.0 m. The Glaciers of Savoy [z].-During the present century much

detailed work has been accomplished on the glaciers of Savoy. As regards the rate of ablation of the glaciers, French workers lay increasing stress on the importance of temperature as the dominant factor. The rate of variation of temperature with altitude was found to be I'C. for 130 m. in sunimer, or 1°C. for 230 m. in winter, giving a yearly mean of 1%. for 180 m. The importance of establishing meteorological stations adjacent to particular glaciers and at different altitudes is also emphasised. Such stations are necessary for the purpose of obtaining monthly records of tempera- ture. The present author maintains, however, that the only reliable records of air temperature available for comparison with the rate of ablation, in a mountainous district, are those recorded a t the ablation station selected on the ice.

From the point of view of the present paper the records of temperatures and rates of ablation of the glaciers of Savoy, some of which cover long periods of time, lose much of their value owing to lack of direct correlation between the two factors [2].

(mean 2.75 m.).

3.-POSITIOS OF ABLATIOS STATIOX OF THE RHOXE GLACIER. The point selected for the ablation station was in the south-

eastern embayment of the Rhone Glacier north of the Belvedere Hotel, and a little north-west of the termination of the path which leads to the Fort and the Furka Path (Plate IX.). This position was easily accessible and was sufficiently isolated to be beyond the influence of heat radiated from the eastern side of the glacier.

+-hfETliOD EMPLOYED. The usual method was adopted for the measurement of the

amount of ice melted a t a given period. A hole three feet deep was bored with a hand auger and a wooden stake inserted, the level of the surface of the ice being marked by a red band of sealing-was which had been dissolved in methylated spirit and was then painted on the stake. At a distance of about a foot above the level of the ice a standardised maximum and minimum thermometer (Negretti & Zambra) was suspended, facing north, and protected from the sun. The method adopted by Forbes of inserting a rod across a crevasse some distance below the level of the ice was considered, hut abandoned as impracticable.

Photograph by G. Slater. South-Enatern Embayment of the Rhone Glacier. Ablation Station. Rhone Glacier, July 27 to

August 15, 1927.

Q.J.R. M e t e o r . Soc., vol. 6 6 , 1929, Plate 1X. 70 jnce page 886.

SLATIIR-SlUDIES ON T.HE RHONE GLACIER, 1927 307

Before commencing the daily recording of the temperature and amount of melting of the ice, an afternoon was spent in noting the hourly temperatures over a period of five hours. The agreement of the results with the formula showed t h e necessity of obtaining hourly records in order to obtain precise results. In view of other investi- gations this was impracticable. A s the average of the maximum and miiiimum temperatures gave too high a value for the average air temperature, some other record was necessary. The most suitable time for the taking of an additional record was about the hour of noon.

~ . - - Z U R I C I I &AIR ?'I;>IPER.ZTURES.

An inspection of the tables of Zurich air temperatures (Dns K h u dev Schweis, 1864-1900) confirms this view, as shown by the following selected table of figures :-

Zurich .%r Temperatures (August). Jiean of

Mas. temp. Noon temp. Min. temp. 2-1 hours. 22.52 21.48 13.0s '7.49

If the mean between the maximum and minimum temperatures be taken, the figure is 17.8, a mean .31 higher than the hourly mean. If, however, the mean be taken of the maximum and noon ,tempera- ture and the resulting figure 21 be averaged with the minimum temperature, the resulting mcan is 17.5.1, or only .05 above the mean of 24 hours.

Assuming the masimum temperature during August to occur i n the afternoon at 2 p.m., the average between the noon and masimum temperatures gives a point of greater precision for the crest of the temperature curve, which is lowered.

P RESULTS OBT.\ISED. The results obtained are indicated in Table I. ; the average daily

temperatures and rates of melting of the ice are plotted in Fig. I. T h e records given in Table I. were taken about noon of each day. As a check to these figures, the noon temperature of the previous day was averaged with the maximum of the succeeding day, and this figure again averaged with the corresponding minimum tem- perature. The average temperature for twenty days by this method was 40.S°F., and the theoretical amount of melting 35.32 inches, as compared with 40.8'F. and 35.58 inches respectively of Table I.

The most striking fact about the table is the confirmation of t h e tentative law of ablation. The average temperature was 40.8'F. or +8.g°F. above the freezing point. Reckoning .2 inches of ice to be melted per day per degree, thc amount of ice melted in twenty days would be 35.2 inches, a result which agrees with the actual .amount of ice melted during this period.

7.-sOURCES , OF ERROR. In view of the variable factors involved, this result was hardly

to be expected. The variable factors are most apparent by esamina- tion of the columns for a particular day.

TABL

E I.-

DAII.

Y TEMPERATURES A

ND

RA

TE OF

hlE

LT

IX'C

OF THE ICE

OF T

HE

I?H

OSE

GI,ACII.:R, JULY 2

6-Ao

GUS

T 15

, 19

27.

1.

Dat

e.

htax

lmui

n tern.

pern

lure

.

"F.

Dat

e.

11.

Ave

raiz

e no

on

tem

pem

ture

.

"F.

1.

htax

lmui

n tern.

pern

lure

.

"F.

11.

Ave

raiz

e no

on

tem

pem

ture

.

"F.

49.0

49

.0

54.0

48

.5

48.7

5 49

.5

5 1.0

51

.0

48.0

52

.2 j

53.0

53.5

51

.0

51.0

53

.0

48.5

50.0

55

-5

48.0

50

.0

49.0

44.6

4-45

41.5

40

.0

40.0

46

.0

46.0

43

.0

44.0

44

.0

46.0

47.2

5

39.5

42

.2 j

45.0

40

.75

41.0

45

-5

40.0

47.0

- 5 1

-73

111.

Ave

rage

of

1. n

nd 1

1.

"Y.

46.8

46

.75

47.7

5 44

.25

44.3

7 47

.50

48. j

o 47

.0

4h.o

48

.17

49.5

50.3

7 49

.0

5 I a3

7 46

.2 j

45.3

7

47.5

48

.12

41.5

47

.75

44.5

47.2

I \'.

Min

imum

tem

- pe

ratn

re.

"Y.

34.0

34

.5

35.0

3-

13

34.0

36.0

36

.5

34.2

5 34

.0

33.5

36.0

36

.0

36.5

33

.5

323

33-7

5 34

4 33

.0

33.0

35

.0

-

31.3

v.

Ave

rage

of

111.

and

lV.

"F.

40.3

7 41

.12

39.6

1 .

39.4

3 40

.75

41.7

5 40

. I2

41

.08

41.5

43.1

8 42

.5

43.9

3 39

.87

38.9

3

40.6

2 41

.31

38.7

3 -1

0.37

39.75 -

42.2

j

40.8

-~

Act

unl r

nte

of m

iolii

ng (i

nche

s ab

ove

flsed

po

int)

.

-

1.3

3.3

5.5

7.0

0.0

0.0

11.0

13

.2

14.6

10

.0

16.5

0.

5

21.2

23

.5

2.5.

j

27.3

2Y

.d

0.0

29.7

3

1.0

32

.7

34. I

3j.2

0.

S

33.2

Dui

lj rn

te o

f m

elri

ng

(inch

es).

-

1.3

2.0

2

.2

1 ..5

2.0

20

2.

2 1.4

1.4

2. j

2.7

2.3

I .8

2.0

1.1

1.3

1-3

1.7

1-4

1.1

35.2

- 1.67

1.

82

1.52

1.

48

8.2d

1.76

2.0

j

I .95

1.

62

1.81

2.23

2.

1 2.

38

1.57

9.M

1.5s

1.72

1.

86

1-33

1.

67

s.15

1.

55

8.33

1.

0

v111

. 'h

mre

tlcal

rat

e of

nelt

inn

baw

d on

te

mpe

ratu

re.

(V.-3?)

x '4.

Rai

n.

Rai

n.

Spon

gy ic

e.

Dry

, w

arm

w

ind.

R

ain.

R

ain

at 4

.20.

R

ain.

R

ain.

Rai

n.

Rai

n.

35.5

8

FIN

AL

RESU

LT = +

8.8"

X .

2 X

20

= 3

5.2

iiicl

ies,

SL.\1‘1<R--S’TUDIES ON 1 H E RHONE GLACIER, 1927 389

Discrepancies due to errors of observation bctween the actual rate of melting and the estimated rate based on temperature can be csplained as follows :-

( I ) ..lverage Noon Temperature.-This figure is based on the averagc of temperatures taken about the hour of noon. Nothing short of hourly records will suffice for the true estimation of the average day temperatures. Hence the average temperatures of column V. are approsimate also. Nevertheless, if the estimation of .2 inches of melting per dcgree above thc freezing point be applied to these figiircs, the discrepancy betwcen thc results and the actual amount of melting suggcsts that thc tenipcrature error is only one o r two degrees.

( 2 ) Estinration 01 tliiily rate o j md/ing.-lIie measui-crncnts of the daily rate of melting of the ice were all taken from the same fised point of the staff in order to obviate cumulative error. In actual practice it was found difficult to measure accurately per day the amount of melting to the degree of accuracy ainied at, i.e., to tcnths of an inch, the method adopted by Mercanton of measuring to the nearest centimetre appearing more practicable. One source of difficulty was the removal of the interstitial ice between ice granules, another the “ spongy ” or cellular structure of the surface of the ice after rain. Occasionally, however, as for esample after a dry warm wind, the surface of the ice became level. If, however, longer periods wcre taken, accurate mcasuremcnts of the rate of melting could be made.

On the whole, monthly periods of measurement of the rate of melting, coupled with daily records of temperature, give the best results.

8. - V A R I .I BLE F.\CTO R s . A ~ i n l y s i s o/ the results as plotted on the Graph (Fig. the the

rcsults shown in the table can be better appreciated by referring to rhc graphs (Fig. I) . These graphs show respectively :-

(a) The actual rate of melting. (b) Thc theoretical rate based on the assumption that .z

inches of ice is melted for each degree of average daily temperature.

(c) A straight line graph showing an average rate of melting of 1.8 inches a day.

(d) X tcmperature graph. The general relationship between the rate of melting and the air

temperature is shown in the graph (Fig. I) by comparing the two curves A B C D and A’ B’ C’ D’, a rise in temperature being fol- lowed by an increase in the rate of melting. This increase, how- ever, is in escess of the theoretical amount of melting based on the temperature alone. This fact is seen in the graph by comparing the curve A’ B’ C’ D’ with the broken curve, more especially between the dates August j thg th (Fig. I ) . This excess in the rate of melting is presumably due to the positive effects of variable factors such as a warm dry wind and warm rain. The succeeding decrease in the rate of melting may also be explained as being due to the negative effect of chilled watcr protecting the surface of the ice

390 SL;\TER-SlUDIES ON 1 H E RIIOSE GI.:\CIER, 19’27 -1

GRAPH snowim RATE or MELTIN6 ff WE ICE

JULY ~~.-AUCUST 15.

Y l O . 1.

SLAT17R-STUDIl~S ON 1 H E RHONI: CI~;\CIIiR, 19?7 391

from the air temperature. There is a general compensation, however, between the two factors.

The figures given in columns V. and VII. of Table I. have been plotted in the two graphs shown in Fig. 2. The maxima of the curves are respectively marked A 13 C D and -4’ U’ C’ D’.

E K u ys 27 $udsy30 31 i 2 3 4 -Y’+Yi s m ii 12 a H ri A B c D

42

30.

w 3

i?

I

0 DAILV RATE OF MELTING,

Fio. 2

It will be noted that the maxima of the curve A’ B’ and D‘ occur in point of time one day later than those of the corresponding curve A. B and D. This “ lag ” may be attributed to the spongy condition of the ice, as measurements of the rate of melting could only be made to the surface of the ice. The position of the apex C’ is a measure of the marked amount of evaporation OF the surface of the ice caused by the warm dry wind.

A comparison between the two curves supports the view that air temperature is the dominant factor in the melting of the surface ice of the glacier.

With this view Sir Gilbert T. Walker, t o whom I showed the paqcr, agrees; he remarks: ‘‘ The variations from day to day indtcate a relationship between the melting and the temperature of the same order of magnitude as is derived from the total melting in the period.” He suggests further that “ the temperature of the ice below the surface must remain at the freezing point, so that, apart from heating by the sun’s radiation, the melting must turn on the temperature gradient of the air close to the ice surface. This will clearly be affected by wind, and in future work it might be well to measure the temperaturc, i f possible, a t a small constant height ahovc the ice.”

~.-GESERAL Cosc~usro~s.

(March 18, 1929.)

The results obtained tend to show that there is a general .

A monthly period would appear to be the most suitable for estimating the amount of ablation and correlating this amount with the average daily temperatures. The slight variations in the minimum temperatures and the form of the temperature curves suggest that hourly temperatures need only be taken during the day and not-for the whole 2+ hours. If this is impracticable, then

6 ) averaging out ” of the variable factors.

392 SL.i’L’13K--S’rUL)Il1S OX THE RHONE GLACIER, 19’37

the method adopted in the present investigation would appear practicable over monthly periods.

For the Rhone Glacier it is essential that there should be a meteorological station. Possibly a t the Fort, adjacent to the Belvedere Hotel, an ablation station fixed on the glacier and pro- vided with a maximum and minimum thermometer could be visited daily by an observer. The rapid rate of melting of the Rhone Glacier suggests the possibility of the removal of the magnificent ice cascade a t some not very distant date. The rate of melting at the base of the cascade where the River Rhone emerges must be considerably higher than that at the ablation station selected by the author. Exact records of temperature and ablation are therefore necessary in order to form an estimate of the future available water supply due to the melting of ice above the cascade.

Reviewing the Rhonc Glacier evidence as a whole, it is claimed that the tentative relationship between the average air temperature and the rate of melting of the ice has been substantiated. The elaboration of this law must be left to others more favourably situated for investigation of modern glaciers. Regional surveys of the more general aspects of climate have been dealt with by Simpson and other meteorologists [ 6 ] .

The application of the law of ablation to the problems of Pleistocene Glaciation is of interest.

Interglacial Periods, which are clearly established in several areas, point to a regional amelioration of climatic conditions. Hence during these periods there was a marked retardation in the accumulation of ice and snow in the gathering grounds. Under such conditions the rate of ablation would be such that regional accumulations of ice from 1,000 to 2,000 feet in thickness could be removed in a period of only a few centuries. With the average known rate of movement of ice, this rapid removal is in striking contrast to the time required for ice to overwhelm rcgional areas, a period which must be reckoned in thousands of years.

IO.-COSCI.USIOS.

In conclusion the author expresses his thanks to Prof. W. W. Watts for facilities for the working out of the results in the Geological Department of the Imperial College of Science, London.

The expenses of this investigation were defrayed by a Govern- ment Grant of the Royal Society, for which the author expresses his thanks.

I I . - sLXJIARY.

Observations in Spitsbergen, 1921, suggested to the author the following tentative relationship between the average air. tem- perature and the rate of melting of the ice:-

t - 32’F. M =

2

where M=thickness (in feet) of ice melted per month (30 days) and t = average monthly temperature ( O F . )

This would become .z inches of ice melted per clay for each dcgrce (F.) above the freezing point under normal atmospheric conditions, wind and rain producing deviations from the normal. \Vith the object of testing this relationship further, abservations were conducted on the Rhone Glacicr in 1927 over a period of twenty days. A hole 3 feet deep was bored in the ice and a rod inserted from which a shaded standardised maximum and minimum thermo- meter was suspended. I t was found that when hourly records of temperature were recorded the relationship given above was corroborated. As the recording oi hourly tcmperatures, however, was impracticable, late morning or early afternoon temperatures ,only were recorded, in addition to the maximum and minimum.

An inspection of the tables of Zurich air temperatures (Dns Klinza det Scl iwciz , 1804-1900) shows that the averagc of the maximum and minimum temperatures gives too high a value to the summer mean, whereas if the mean between the noon and maximum temperatures be first obtained, and then the mean cal- culated between this figure and the minimum temperature, the approximation to the true mean is more correct. This method was accordingly adopted. The average temperatures (July 26 to August IS) were as follows :--Maximum 50.6’F., minimum 34.s°F., noon 43.79’F. giving a daily average of 8.8’F. above zero. Assuming the rate of .z inches of ice melted per day for each degree, the total amount melted would be 35.2 inches, a figure which is confirmed by actual measurement.

I~IULIO(;RAPHY. 111 1859. Forbes, James D., “ Occasional Papers on the

Theory of Glaciers. ” Edinburgh. [ a ] 1y9 , ’10, ’12, ’22, and ’25. “ Etudes Glaciologiques en

Savoie.” MinistCre de 1’,\griculture, France. 131 1916. Hoel, Adolf., “ Observations sur la vitesse d’ecoulc-

ment et sur l’ablation du Glacier Lilliehook au Spitsberg, 197-19IZ.” Vidcnslr, Scltlk., Skr. I., d la t l i -Nut . KZ.’ Oslo, No. 4.

141 1916. RIercanton, 1’. L., ‘‘ Mensurations au glacier du KhBne 1874-1915.” Commission des glaciers de la SocietC helv6tique des Sciences naturelles (S. H.S.N.), Zurich.

951 1925. Slater, George, “ Observations on the Nordenskiiild and Neighbouring Glaciers of Spitsbergen. ” (Oxford Univ. Expedition to Spitsbergen, 1921). Journal of Gcology, 33, No: 4, pp. 408-44G. Also in “ Spitsbcrgen Papers,” Oxford Univ. Press.

161 1927. Simpson, G. C., “ Past Climatcs.” Q.J.R. N e t c o r . S O C . , 53, 1927, PP; 213-232.

DISCUSSION.

Sir GILBERT \VAJ.KER thought it interesting that, in spite of the part played hy wind in increasing evapration, the effect of temperature should be equally shown in the integral over a period and in the changes during the period.