Water temperature during the melting of lake ice

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Water temperature during the melting of lake ice

Williams, G. P.

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S e r TH1

a N21r2

no. 4 2 1

C . 2

NATIONAL

RESEARCH

COUNCIL

OF

CANADA

I

WATER TEMPERATLIRE DURING THE MELTING

OF LAKE ICE

G.

P. WILLIAMS

.

-

--

.

ANALYZED

REPRINTED FROM

WATER RESOURCES RESEARCH VOL. 5, NO. 5. OCTOBER 1969

P. 1134

-

RESEARCH PAPER NO. 421

O F T H E

DIVISION

OF BUILDING RESEARCH

i 2

'RICE 10 CENTS

OTTAWA

SUR LES LACS

SOMMAIRE

L a t e m p e r a t u r e de l ' e a u et 1 1 6 p a i s s e u r de l a glace ont Bt6 m e s u r e e s durant l a pCriode de l a fonte 'a Bennett Bay, White Lake, Ontario. L e s t e m p 6 r a - t u r e s de l ' e a u s e s o n t 6levCes j u s q u 1 8 7 . 5 " C . s o u s l a couche de glace fondante. L a c h a l e u r r e q u i s e pour r h c h a u f f e r l l e a u s o u s l a gla:e et l a f o n d r e e n t r e l e s deux f a c e s g l a c e - e a u a 6t6 calcul6e 'a diffdrentes p e r i o d e s et c o m p a r d e a v e c l a c h a l e u r disponible dmanant de r a d i a t i o n s o l a i r e qui pCnCtrait l a couche de glace. On a c o n c l u d e c e s c a l c u l s que l a r a d i a - tion s o l a i r e pCn6trant l a glace a c a u s 6 d e s t e m p e r a - t u r e s d ' e a u r e l a t i v e m e n t 6 l e v 6 e s observCes s o u s l a g l a c e fondante.

\\'A?'ER R E S O U R C E S R E S E . \ R C H O C T O B E R 1969

Water Temperature

clzwing

the

Melting of

Lake Ice

G . I?. WILLIAMS

Arntiond R e s e a ~ c l ~ C'o~tncil of Canada, O t t a ~ c n , O7zta~i0, Catlada

Abstract. Watrr tcmperatu~c and ice tliicl;ncss wcrc measurctl during the Ice mclt period

a t Bcnnctt Bay, Whitc Laltc, Ontario. Waler t~mpcmlurcs were as l11:11 as T.5"C ~ ~ n d c r the

melting icc cover. The heat ncctled lo nrarm the water untlcr thc ice and io mclt ice a t the ice-water intcrface mns calculated for d~ffcrcnt pcriods ant1 comparctl ~vilh tllc heal av:lilablc from solar radiation that pcneiratcd the ice covcr. I t was concludct! from thcsc ct~lculntions

that solar r:ldiation pcnctrntlng lhc ice causccl Lhc ~.clul~vcly high watcr t i ~ m l ~ c r l ~ r c s obscrvccl

under the melting ice.

I n a recent paper Bilello [19GS] reported that water temperature underneath the ice cover in a shallow lalre decreased substantially during tlie ice t11a.r~ period. I n contrast t o Bilello's observations, water telnperature unclcr :ln ice cover a t 'i5'11itc Lake, Ontario, increased substantinlly during the thaw period with tem- pcrntures as liigh as 7.5" C being rccorclcd. T h e plu'pose of this note is t o report and interpret tlicse observations.

During 1967 and 196s water tcmpcraturc and icc tliiclr~icss mcasureincnts were niacle during tlie ice melt period a t Bennett Bay, White Laltc, Ontario (Figure 1 ) . This bay, about 1.G lrm long ant1 0.8 Bm wide, has a n~asumuin depth of about 9 mctcrs. VTater tcinperature profiles were

obtained once a meek ivith thermistor tempcra-

turc sensors a t three sites locatccl about 100, 200, and 500 mctcrs from sliore. 'i'rater depth ranged from 3 meters a t the site near shore t o about nine rneters a t the site farthest out in the bay.

All calculations presented i11 this note mere made using tlic water temperature observatio~is obtained a t tlic site 100 meters from sllore

(Figure 2 ) . Similar temperature profiles were

obtained a t tlie other sites (Figure 3 ) .

T h e heat gain in a column of water of unit area under the ice for 7-day melt periods was calculated as follows:

Qm =

C

which equals summation of lieat gained in layers of water under the ice (cal/cm2) where

C,, volumetric heat capacity of water

(eal/cn13"C) a t the mean temperature of the layer;

AT, mean change in temperature within specific layers of the column during

7-day periods ("C);

AIL, thickness of layer (cm). 30-cm-thick layers mere used.

Tlic lieat contributccl bv the xvatcr for t h e melting of icc a t the ice-mtcr iiltcrface was

cstiinated with tlie follo~>-ing formul:~ :

&Val lieat contributed by water for melting

ice (cal/cm?) during 7-day ty~eriods;

1c,,

,

water (= 0.0014 cal/cm°C sec);

AT/AZ, average temperature gradient in 5-cm

layer of water inlinediately below ice-water interface ("C/cm) during 7-day period.

This formula assuincs t h a t heat can only be

transferred b y molecular coilcluct~oil tlirougli t h e

thin stable layer of water a t the ice-water inter- face.

T h e results of tlie preceding calculatioris a r e

presented in Table 1 . T l ~ e sum of Q,,, and Q ,

represents the total lient supplied to tlie lvater during tlie melt periods.

BRIEF REPORTS 1135

Pig. 1. Location of Whitc Lake, Ontario. (luring tllcsc nlclt periods coulcl linve bcen sup-

plied from the following sources:

1. sno~vmelt runoff

2 , lalcc bottom secliments

3. ground-water flow through the bottom

sediments

4. lateral flow of heat uilder the ice from

open water ncnr tlie shoreline

5. solar radiation penetrating tlle ice cover. Snolvmelt runoff can be eliminated as a major source of heat; runoff from the surrounding land, flolving laterally under the ice, ~vould 1,robably decrease thc ten1peratul.e of thc water,

as was tlie case when observed by Bilello. There are no well-clefinccl streams or creeks flowing into the lake nt tlie site of tlie observations.

Heat flow from lnkc bottom sediments in April ~voulcl be slight because the heat storccl in this material would be clepletecl during tlle winter months. Bilello cstimatecl t h a t in December heat concluctecl from bottom inaterid was only

about 12 cal/cm2/24 Ilr. This value agrees

reasonably well wit?] ATyb~ant's [I9591 values for lieat flow from typical bottom material dur-

ing tlie early minter for latitudes 50 to 60 N.

Nybrant consiclercd that heat flow from bottom inatcl.ia1 in April would be almost negligihle.

1136 BIiIEF REPORTS

I I I I i l I

-

- -

I I I I I I

0 1 2 3 4 5 6 7

W A T E R T E M P E R A T U R E . - C

Fig. 2. Wnter tem~ernturc profilcs uilcler ice cover

100 meters from shores.

T E M P E R A T U R E , OC

0 1 2 3 4 5 6 8

W A T E R

10

Fig. 3. Watcr tempcrature profiles under the icc

cover.

T A B L E 1. IIcnt Supplicd to the Wnter during Melting of t h c Icc Cover on White Lnke

I'eriod of O,,, Qur Totnl O b s c r v n r i o ~ ~ s cnl/cm? cnl/cm? callcm'

1067 SO March- 6 April 55 414 460

6 -4pril-13 April 410 584 994

1968 27 March- S April 572 500 1072

There was no evidence t h a t heat from ground- water flow through bottoin sediments was suf- ficient to increase water temperature eignifi- cantly. Water tempcrature profiles under t h e ice cover before the active thaw period were typical for laltes a t this latitude wit11 no incl~cation of substnntial heating of the bottom water layers by ground-water flow (hlarch 30 profile, Figure

a ) .

Solar radiation warming the open water near the shoreline could result in lateral flow of water under the ice cover. Dilring the periods of observation tlle area of open water near the

sliore n a s not estensive, varying f ~ o m 1 t o 2

meters in nriclth. Calculations indicate t h a t heat from this source did not contribute effectively to t l ~ e obbel.vec1 increase in water teml~erature [under tllc icc cover.

S o ~ r ~ c npprosimatc calculations were carried

orit to ddcrinine ~ v l ~ e t h e r the heat available

from sol:lr racl~ation t h a t penetrated t h e ice cover woiilcl be sufficient t o esplain the increase

In tcmpcrature The amount of racl~ation penc-

tmting tllc lee cover was csti~nated from the

followilig formu1:i: .

I,, solar racliatiorl penetrating to depth z(cm)

t

I,, solar radiation received a t the ice surface

(cal/cm?) :

A,

Incoming solar radiation d u r i ~ ~ g the weelrly

observat~on periods was estimated from short- wave radiation recorded a t Ottawa about 40 miles east of White Lake. The percentage of incoming solar radiation reflected from the sur- face was nssu~llecl to be 30%, a reasonable value for melting ice.

Two values of estinction coefficient were used, 0.01 and 0.02, which are about the range of

B R I E F REPORTS 1137

ice in Wisconsin lakes. These values are con- siclerccl reasonable, for during 11otli seasons the ice covers were essentially clear for the lo~ver

~,TTO thirds of tlieir thicltness b u t had some air

l1ul111lcs entrapped in the upper layers.

T l ~ e calculated amounts of radiation penetmt-

ing tlle ice cover for the melt periods are given

in T a l ~ l e 2.

These values compare reasonably well ~ v i t h

the previously calculated total heat

(Q,,,

+

gainecl by the water cluring the observation l~eriods. I t is concludetl, therefore, t h a t solar mtliatioli l~cnetrnting the ice caused the rela- tively 11igl1 ~ r a t c r tempcratures observed a t TVliite Lalte.

Water teml>erntuse under a melting ice cover will be highly variable l~ecause of variations i n the extinction coeficient of ice. The percentage of radiation that penetrates different thicknesses of snolv nnd ice for tlilrcrellt extinction coef-

ficients is illustratctl in Figure 4. Thc range

shown for extinction coeficients is bnsetl on values reported in the literature [Geiger, 1965; Scott, 196-1; Lljo1.i~ and Stoiber, 19591. Figure

4 s h o ~ ~ s t h a t n large proportion of the in-

coming solar radiation ~vill penetrate clear ice of collsidcrable tliicltncss, whcreas the amount

penetrating b u l ~ b l y ice or sno~v-col-ercrl ice Inny

be allnost negligible.

Fieltl obser~~ations tend to confirm that water

te~npcratures untlcr melting ice will vary tle- pcl?tling on tllc n m o ~ n i t of solar racliatio~l th a t can pcnctrate t l ~ c ice. The masirnunl water tcnlperature mcasurctl by nilello under a melt- ing laltc ice cover that was two thirds bubbly ice u-as about 2.0 to 3.0°C. I n contrast, water tempcratures as high as 7 5 ° C reported in this note a~lrl clscwherc in ihc literature [Rill, 19671 arc probably not uncommon if significa~lt a m o ~ m t s of solar radiation can penetrate through melting hlte ice. I n permanently ice- covered lakes, bottom tcmpemturcs as 11igh as 25°C have been attributed to solar hcnting

10 20 30 40 50 60 70 80

I C E T H I C K N E S S , c m

Fig. 4. Per ccnt radiation pcnetl~~ting ice covers

for cliffercnt estinction cocflicicnls, A.

[TTTilsoll nr~cl Wellnzalz, 19631. Sonle of the im- plications of solar hcating for the stability of tile water under tlic ice h a r e been discusscrl by TBoodcoclz [1965].

T h e rate a t ~vhicll ice clears from n lake call

be influenced by the solar heating of water

under a melting ice cover. Wind may cause a free ice slleet to oscillate both horizontally ant1 ~ e r t i c a l l y and m i s tlie water bclo~v [Bilello. 19681, resulting in an increased rate of melting.

If the wind action continues and tlie ice is thin,

i t will s t a r t t o hrcalr up nntl melt mpitlly by

mising freely \\-it11 the water l~rcviously ~ v a n n c d

by solar radiation. I n 1968 a t Bennett Bay the

n-ater was cooler by about 2°C to a consitlcrable tlepth (April 9th profile, Figure 3) immetliately

after the ice liar1 clenretl fro111 the l ~ a y , indicating

t h a t several centimeters of ice were mclted by

~ n i r i n g \Tit11 water under the ice. Wil~tl speetls of

10 to 14 mph a t n height of 3, meters Tvere re-

TABLE 2. calculated Radiation Penetrnti~ig the Ice Cover during Melt Periods

hIenn Ice I ,

Period of Thickness 10 (cal/cm2)

Observations (em) (cal/cmP) A = .01 1 = .02

1967 30 Narch-6 April 48 1660 1030 600

6 April-13 April 35 2000 1410 962

1138 BRIEF REPORTS

corded during t,he 24 hours prior to the final clearance of ice from t h e bay.

dcknowletlgn~eizt. This is a contribution from the Division of Building Research, Kational Re- search Council of Canada, and is published with the approval of the Director of the Division.

REFERENCES

Bilello, M. A., Water temperatures in a shallow lake during ice formation, growth, and decay,

W a t e r Resour. Res., 4(4), 749-760, 1968.

Geiger, R., T h e Climcite 11iear the Ground, 611 pp., I-Iarvard University Press, Cambridge, Mass~chusetts, 1965.

Hill, H., A note on temperatures and vater condi- tions beneath lake ice in spring, Limnol. Oceccnog., 1R(3), 550-532, 1967.

Lyons, J. B., and R . E. Stoiber, The absorptivity

of ice: A critical review, R e p . 3, C'o~at~act AF

19(GO4), Dartmouth College, Hanover, R e ~ v Hampshire, 13, 1959.

Xybrant, G., Water temperatures in a pond and its dependence on flom, S e n ~ i i ~ a r o n Ice Prob- lems i n Hydraulic Structures, 8th Congress, International Association for Hydraulic Re- search, Montreal, 1959.

Scott, J. T., A comparison of the heat balance of lolces in minter, U n i v . W i s c o n s i i ~ Dep. ikleteorol.

T e c h . R e p . IS, 138 pp., 1964.

Wilson, il. T., and H. W. Wellman, Lake Vandn: An antarctic lake, Nature, 4860, 1171-1173, 1962. Woodcock, -4. H., Mclt patterns in ice over shal-

low waters, Limnol. Oceaizogr., 10, R290-R297, 1965.

(Manuscript received February 10, 1969 ; revised ilpril 25, 1969.)

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