a practical method of predicting sea ice formation and growth (1954)

8/4/2019 A Practical Method of Predicting Sea Ice Formation and Growth (1954)

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TECHNICAL REPORT

A PRACTICAL METHOD OF PREDICTINGSEA ICE FORMATION AND GROWTH

OWEN S. LEEand

LLOYD S. SIMPSONApplied Oceanography Branch

Division of Oceanography

SEPTEMBER 1954

U. S. NAVY HYDROGRAPHIC OFFICEWASHINGTON, D. C.


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ABSTRACTA technique for predicting ice formation and growth is pre-sented. The ice potential calculations originally discussedby Zubov and Defant form part of the method, as do thestandard heat budget equations developed by variousauthors. In addition, new formulas are derived for com-puting ice growth in terms of known or predicted oceano-graphic and meteorological data. The method is applied tothe problem of predicting the general features of the icedistribution in the Baffin Bay- Davis Strait area for theseason 1952-53. It is pointed out that use of this methodmust be limited to open-sea areas where winter and notpolar ice is the dominating feature. However, the techniquehas important applications to estimating the general icefeatures of such areas several months in advance.


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FOREWORD

The increasing importance of defense installations innorthern areas has increased greatly the responsibilities ofthe U. S. Navy in supplying bases in Arctic waters, where seaice is often an operating obstacle. The Hydrographic Officeis charged with the responsibility of developing and testingtechniques for observing and forecasting sea ice conditions.Standardized techniques for observing, charting, and reportingsea ice are now in operational use by the Navy, as described inpublications issued by the Hydrographic Office. Heretofore,techniques for forecasting the formation, growth, and movementof sea ice have not been published by this Office. This publi-cation describes a method of long-range forecasting of ice for-mation and growth. Since this technique is still in the develop-mental stage, the Hydrographic Office welcomes comments as to itsoperational value.

//. B. COCHRANyCaptain, U c S. NavyHydrographer

iii


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DISTRIBUTION LIST

CNO (Op-03, 03D3, 31, 316, 32, 33, 332, 04, 05, 533, 55)BUAER (2)BUSHIPS (2)BUDOCKS (2)ONR (Code 100, 102, 410, 416, 420, 430, 464, 466)NOL (2)NEL (2)NRL (2)CGMOPDEVFOR (2)CCMSTS (2)CODTMB (2)ARCWASUPNAVACAD (2)NAVWARCOL (2)NAVPOSTGRADSCOL, Monterey (2)COMDT COGARD (IIP) (2)USC&GS (2)CG USAF (AFOOP)CGAWS (2)CGNEAC (2)USAF CAMBRSCHLAB (2)USWB (2)CIA (2)BEB (2)SIPRE (2)ASTIA (2)ARTRANSCORPCE (2)INTLHYDROBU, Monaco (2)ARCRSCHLAB, COL, AlaskaARCINSTNA (2)WHOI (2)SIO (2)UNIV WASH (2)TEXAS AM (2)CBI (2)

iv


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CONTENTSPage

Foreword . iiiDistribution List ivFigures vTables viA. Introduction 1B. The Ice Potential of a Water Column 1C. Method of Computing Date of Ice Formation 5D. Method of Computing Ice Growth 7E. Use of the Ice Growth Tables in Forecasting 10F. Baffin Bay-Davis Strait Long-Range Ice Forecast for

Season 1952-53 13Conclusions _ 13Bibliography 27

FIGURES1. Oceanographic Plot for Station #37 42. Ice-Potential Curve for Station #37 . 63. Ice-Growth Forecast for Station #37. 124. Forecasted and Observed Ice Boundaries in Baffin Bay

and Davis Strait for the Season 1952-53 H


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TABLESPage

1. Oceanographic Data for Station #37


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A. INTRODUCTIONThe expanding program of ice observation and forecasting at the

Hydrographic Office has emphasized the desirability of long-range iceforecasting. There are many phases of the ice program for which longrange forecasts giving advance estimates of ice conditions of as muchas 150 days are required. This paper deals with long-range forecastingof ice thickness in open seas whose salinity and density remain rela-tively constant, such as Baffin Bay and the Labrador Sea.

An operational method of forecasting for a long period must beeasy to use, require a minimum number of involved calculations, andyield forecasts of reasonable accuracy. Most formulas previously devel-oped have been complicated expressions which are not suited for opera-tional use. In developing the following method, the goal has been toperfect a technique from which quantitative results can be derived witha minimum of computation and observation.B. THE ICE POTENTIAL OF A WATER COLUMN

The severity of an ice season depends, among other things, upon theamount of thermal energy stored in the water mass and upon the rate atwhich convective mixing takes place. It is necessary to select a modelof convective mixing which will explain the variation in the thermohalineconditions caused by heat removal and ice accretion. The method proposedby Defant (1949) and by Zubov (1938) of computing the ice potential andpotential heat loss has been adopted as a basis for the present forecast-ing technique.

Before a forecast can be made, an analysis of the properties thatinhibit ice formation and growth must be perforated. Oceanographic meas-urements within the area in question must be secured in order to obtaininformation about salinity and thermal energy stored within the watermass. Unnecessary computation can be avoided by making the measurementsat a time after the heat flux reverses, when thermal energy is beingcontinually removed from the water. Otherwise the amount of heat whichwas added to the water column prior to the reversal of the heat fluxwould have to be computed before the method of Defant and Zubov couldbe utilized.

Establishing the ice potential of a given water column requiresonly the temperature and salinity at N levels within the column. Thecolumn is divided into (N-l)jLayers and the mean temperature (Tn),salinity (Sn), and density (crn), are computed for each layer. Themixing model, as defined by the method of Defant and Zubov is constructedby finding the rrvjan temperature and salinity of the surface and secondlayers, i.e.,

hlh = i,2 , hJ-h = Tlf2 m


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The column is then said to be partially mixed down to the second level.Complete mising is achieved by cooling the partially mixed column untilits density,


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Aa the mixing model is developed, each layer will .yield a certainamount of potential heat loss, q^, and eventually, when the temperaturesare low and the densities are high, each layer will yield a certain masaof potential ice ( ) associated with convective mixing down through thecorresponding layer. Thus it is possible to construct the very useful"potential curve" (Figure 2) from corresponding

I&Z=l,(h) and QT(h)=QT(h)-Q , where V / V2 ' (3)The potential curve is plotted, QT starting from zero within the layerwhere ice first appears. The remainder of the %% Q , which is lost beforeice is formed, determines the date of ice formation. The reason for

taking QT as zero at this point becomes evident when one considers thelower limits of the integrals in equation (13). Obviously some questionarises as to the exact quantity of heat that has been removed at thetime ice is first formed. There is, of course, some error introduced,but it is not large as long as the water temperatures are near thefreezing point and the water column is divided into layers of suffi-ciently small depth, for example five to ten meters. Recent work onthe same type of model as Defant's has yielded exact values of the 0^.which must be removed before ice is formed, thus determining the properpoint to start accumulating the Qjp for the potential curve (Brown,1954)

In order to illustrate the computation of the ice potential andthe drawing of the potential curve, a typical oceanographlc stationis used as an illustratioa. Station 37, at 66 N, 58 W, was occupiedon 3 October 1952. A ploc, of the oceanographlc variables at this sta-tion is given in Figure 1, and the complete numerical data are shownin Table 1.

TABLE 1Oceanographic Data for Station #37(66N, 58W), 3 October 1952

Depth Tempe rature Salinity%o DensityAnomaly (t)m. L. gm/liter0.56 32.37 25.98

5 0.10 32.36 26,0010 0.61 32.39 25.9920 0.73 32.47 26.0530 -0.41 32.78 26.3650 -1.65 33.08 26.6475 -1.61 33.69 27.1399 -2.13 33.69 27.14

148 -0.52 34.04 27.38197 1.52 34.21 27.40296 0.08 34.34 27.59394 -1.71 34.52 27.81


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o 25.00A 31.00 26.0032.00 27.0033.00 28.0034.00 29(35.D d3 ~l -1 I 2 3 4 5 6 7 8 9 10 II 12 13 14 15 16 1

20406080100

120

140

160

!80

200220

240260280300320

340

360380400 a T EMPE ?ATUF ECO ENSIT /(""t) ' SALI VJITYCUi

FIG. I OCEANOGRAPHIC PLOT FOR STATION NO. 37, 66N 58W, 3 OCTOBER 1952.


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From these data the ice potential has been calculated by the method ofDefant and the results shown in Table 2A, Finally, the ic potentialcurve for Station 37 is shown in Figure 2 It will be noted that theice potential curve is by no means a straight line or a smooth curve.In fact, for this station, the heat loss necessary to form a givenamount of ice varies considerably. For this reason, the actual fore-casting for this station is difficult, for a small additional heat lossat about 2 kg. cal. causes the formation of a large amount of ice. Inthis respect the example shown is not typical of may stations wherethe ice potential curve is quite regular and smooth j however., it isincluded to illustrate the kind of difficulties encountered in practice.In addition, the curve is atypical because Q , the heat loss necessaryto bring about formation of ice was found exactly at 25 meters when thetemperature of the completely mixed layer (1-4, Table 2B) first droppedto -1.8 C. In general, Q cannot be so easily determined.C* METHOD OF COMPUTING DATE OF ICE FORMATION

There are two acceptable methods of computing the date of iceformation. Since the amount of heat that must be lost before ice isformed is known from the ice potential computations, it is only necessaryto compute the time required to lose this heat. One method is to makeactual observations of the heat loss per day per square cm, and thus tofind the mean heat loss which is representative of a given area. Theother method is to compute the total heat loss by consideration of theclimatological data, the sun's altitude, and oceanographic data. Forthis purpose the only known formulas are those of Jacobs (1942), whichyield rates of heat loss of the right order of magnitude in the Arctic,although they were specifically derived for middle latitudes.

Jacobs' formulas for computing heat losses aretQab = .025 a [.29 +.71 (!-__)] ft- r)t,t in minutes (4)Qb= .94 [eff. Qb U- .0083c}]

Q e = 145.4 w(ew -e a )| j+ #01

u t in minutes (5)fTw-Jkllt , t in days, (6 )* "w @oiJ

where 2Q . = total Incoming radiation- in gm, cal/cm,ab ?Q. - total back radiation in gra. cal/cm. ~q - total heat loss due to evaporation in gm, cal/cncc a mean altitude of the sun in degress,c mean cloud amount in percent,W mean wind velocity in knots,


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uu

ICE THICKNESS IS PLOTTED AGAINST HEAT LOSSAFTER ICE FORMATION. DEPTHS OF CONVECTIONARE INDICATED BESIDE EACH POINT (TABLE 2 )150 m

OlOOm

075 m

jJ070m~r065m

rno

'

BO

70

( i55m

50403020

10

n

50md>45m

yv0ni

rreom

^5mI 2 3 4 5 6 7

iEAT LOSS AFTER ICE FORMATION IN KILOGRAM CALORIES (QT-Q )= Q TFIG. 2 ICE-POTENTIAL CURVE FOR STATION NUMBER 37.


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&W - vapor pressure of the water in inches Hg 0i,ea - vapor pressure of the air in inches Hg,,Tw = temperature of the water in degrees F,Ta


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I k,l,Jkiln ATthen AT = AT,U+T-rf r AT, - 1~ i (9)

Mi

Then (7) becomes: d(Ql +QT ) k IAT (10)1jj^

Substituting Q|=/o-Kl. into ( 10 ) ^o denotes ice density)

p,ku^L s _J^L_ (11)' dt dt l.hSJk]

^ K{

l +^} 1 ? dl ' + {1 +^} 1 S dQT ==k J ATdf (12)/l|(h) AKk, A (h) rQT(h)

P] k[ '^(zjdiiiz)^ r 'isdi,(z)+ r T i,(z)dQT (z) +'o s "'0 "'O

ii- r T isdQT(z)=k r r MdtK s ^0 "'t,, (13)

,Qjh)^l^(h)/^lsl.(h) + r T l 1 (Z)dQT (Z) +4Lls QT (h) = k i /et(TF -T)dt.(U)*- s 0 S


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The right-hand expression in equation 14 is usually denoted by thetitle "degree-days of frost;" A degree-day of frost la defined as aday with a mean temperature 1-degree Centigrade below the freezing pointof sea water. While the freezing temperature of sea water varies withsalinity, it is here assumed to be -1.8C. A degree-day of frost isthen 1 day with a mean temperature of -2.8C. Degree-days of frostusually are accumulated for forecasting over periods of 15 or 30 days*By giving the following values to some of the terms in equation 14*

* i - 0.9K = .080 gm

ki , .389 JfcCfii1 cm C dayk - 062 K Cal >ks ~ ot"d cm C day*

the formula can be used directly to forecast the ice in terms of degree-days of frost ,

f Q (h)

l[(Z)dQT(Z)the number of degree-days of frost required to form 1. centimeters of icecan be computed.

To eliminate the necessity of computation, the end results of thederivation have been presented in the form of tables (Tables 3-12). Inaddition the integral

-QT(h)fl[(Z)dQT(Z)

had to be evaluated by approximation methods. It was found from the majorityof potential curves that the integral could be approximated as

H~2~ QT(n).


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The error Introduced was found to be small unless the water temperaturewas unusually high, and in most cases ice will not form under such condi-tions. Since the potential curve 1^(Qt) must always be plotted, it Isreadily apparent when the above approximation is invalid; in this situationthe formula can be used. In order to facilitate substitution of theactual integral for the approximation, an auxiliary table (Table 13) isincluded whicn gives the degree-days of frost associated with variousvalues of 1^ and Op. If the potential curve is very Irregular, Table 13is entered, and by comparison with the degree-day figure computed froman average 1^, one can determine the amount of error introduced into thetotal* Most frequently this will be found to be small, since the potentialterm is only one of four separate factors contributing to the total $ how-ever, the actual value can be added or subtracted and a more accuratefigure secured.

The form of equation 14 which was used in the tables is

The degree-days of frost for fixed 1 8 0, 2*5, 5, 7.5, 10, 15, 20, 30,40, and 50 cm. are given in Tables 3 to 12. The concept of degree-dayshas an advantage over one of calendar days because of its versatility asfar as forecasting is concerned. An ice forecast in days is difficultbecause It requires a forecast of air temperatures as well as ice growth,while the degree-day forecast permits ice growth forecasts which fit allconceivable temperature variations.E. USE OF THE ICE GROWTH TABLES IN FORECASTING

Forecasting the ice growth in a given area requires the followinginformations (1) oceanographic data taken after the water mass beginsto cool and prior to ice formation, (2) the date of Ice formation, and(3) an expression relating ice growth to degree-days of frost for thegiven area. With this information the forecaster can. then proceed tomake a forecast for the entire season. The procedure is as follows?(1) the ico potential of each oceanographic station is calculated andthe ice potential curve (example, Figure 2) is drawn; (2) from availablemeteorological and oceanographic data, the date of ice formation isdetermined; and (3) the forecast is made in terms of degree-days offrost.

Since the calculation of the ice potential, the date of first iceformation, and the ice potential curve have been previously explained,the remaining discussion will describe the preparation of an actualforecast. As before., Station #37 is used as an example. The ice poten-tial curve for this station is given in Figure 2. In order to draw theice forecast curves for this station it is necessary to read the icethickness figures corresponding to integral values of Qp from the Icepotential curve. The degree-days of frost corresponding to each combi-

10


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nation of lj. and QT values are read from each of the tables 3 to 12. Aplot of ice thickness vs degree-days of frost is made from each set ofvalues obtained from the graphs, and a smooth curve is drawn for eachvalue of snow depth (lg ). An example of a completed forecast is givenin Figure 3. In Figure 3,0= 1 corresponds to an ice thickness of 27cm. and Qp a 2 to an ice thickness of 72 cm. on the ice potential curveof Figure 2. To convert the completed forecast into a time forecast themeteorologist must provide temperature and snow depth forecasts in orderto secure an ice thickness forecast of 120 to 150 days for this station.

Now let us suppose that the date of first ice formation at Station#37 is 12 November and that the meteorologist provides a forecast,including the following data for the succeeding months

Mean Snowp , . Temperature Degree-Dy DepthPeriod ^0c) of Frost (cmj

12 - 15 Nov. -5.8 1616 - 30 Nov. -4.8 451-15 Dec. -8.8 105 2.516 - 31 Dec. -7.8 96 2,51-15 Jan. -9.8 120 7.516 - 31 Jan. -18.8 272 7.5

The ice thickness for any given date may be found from the above dataand the forecast curve.

During the period when the snow depth is zero, the growth of icewill be along the upper curve on Figure 3} on 30 November, the finalday with no snow, the total of degree-days of frost is 16 4- 45 or 61and the ice thickness will be 17 cm. (point A on Figure 3).During the month of December the ice grows under a snow depth of

2.5 cm. from a starting point of 17 cm. This point is marked A*. DuringDecember a total of 105 plus 96 or 201 degree-days of frost is counted^so that it is necessary to follow the curve lg = 2 5 for 201 degree-daysof frost beyond point A 1 , or to point B. At point B, reached 31 Decemberthe ice thickness will be 35 cm.

Similarly, during January the ice grows uhder a snow depth of 7.5cm. for 120 plus 272 or 392 degree-days beyond the point B 1 correspondingto an ice thickness of 35 cm. On 31 January the point G is reached, andthe ice thickness will be 53 cm. This constitutes an operational fore-cast, as the user of the forecast can determine the ice thickness on anyday between 12 November and 31 January by counting the number of degree-days of frost and noting the snow depth applicable to the situation,,

11


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!V |_UJ4.

U. oo UJK

>- O< U.n II l-UJ 5hi ooc n-o oliJQ LUo

tod

(ujo) SS3NX0IH1 301

12


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P. BAFFIN BAY-DAVIS STRAIT LONG-RANGE ICE FORECAST FOR SEASON 1952-53.During early autumn, 1952, oceanographic obsenations were taken at

the locations shown on Figure 4 The method explained previously wasemployed to forecast the ice formation and growth of these locations.The dates of ice formation were computed and are shown beside each sta-tion. Since the thermohaline structure at some of the stations was suchthat no ice would be formed, it was possible to delineate the theoreticalextreme ice boundary shoivn as a heavy line in Figure 4 This boundaryagrees very well with the boundary which was actually observed in latMarch and early April 1953* (shown as a dashed line in Figure 4) exceptfor the occurrence of ice south of Stations 39 and 40. It is possiblethat ice which was observed at these two stations was not formed there,but had drifted from nearby areas of ice formation,, The dispersion ofice near the observed boundary in this area indicates that the iceactually was formed outside the area.CONCLUSIONS

The methods of Zubov and Defant for ice potential calculation haveproved in practice to give reasonable answers for open seas and for in-shore areas where local variations in the physical properties of thewater are not large. In harbors and areas where runoff is important,changes in salinity and density are so rapid that it is difficult toattach a meaning to an average value of these parameters. Hence anyice potential calculation based on one or a few observations in a harbormay give a potential ice growth which is unreasonably high or low for asingle season.

The forecast of ice growth based on the ice potential can be usedonly during tho period when ice thickness is increasing,. No theory hasbeen included which accounts for decreasing ice thicknesses during thebreakup period. Indeed, no mathematical theory has yet been developed.for the breakup of ice.

Many refinements of the method presented in this paper are possible.Some of them are discussed in a paper by Brown (1954). The method describedhere was used to forecast during the 1952-53 ice seasonj the forecast provedto be satisfactory. The most 'important advancement discussed in this reportis the use of the ice potential as a basis for forecasting ice growth.

13


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80 75 70 65 60 55 50 45

FIG. 4. FORECASTED AND OBSERVED ICE BOUNDARIES IN BAFFIN BAY ANDDAVIS STRAIT FOR THE SEASON 1952-195314


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TABLE 2ICE POTENTIAL CALCULATIONS FOR STATION #37(66N,58"W), 3 OCTOBER 1952

DepthMeters

5101520253035404550556065707580859095

1001502003004.00

TC S o

.56

.10

.61

.67

.73

.15-.41-.86-1.18-1.50-1.65-1.65-1.62-1.62-1.61-1.61-1.72-1.80-1.80-1.80-1.80-0.511.500.06-1.75

32.3832.3632.3932.4132.4732.6232.7832.8632.9433.0133.0833.2033.3633.5033.6033.6933.6933.6933.6933.6933.7034.0634.2134.3534.53

25.9826.0025.9926.0026.0526.2026.3626.4326.4826.5426.6426.7626.8826.9827.0727.1327.1427.1427.1427.1427.1427.3827.4027.6027.82

Layer DepthNo. (Meters)

0-1010-1515-2020-2525-3030-3535-4040-4545-5050-5555-6060-6565-7070-7575-8080-8585-9090-9595-100100-150150-200200-300300-400

TC

.54

.70

.44-.13-.64-1.02-1.34-1.58-1.65-1.64-1.62-1.62-1.61-1.66-1.761.801.801.801.16.50.78-.84

Mean ValuesS %o32.3832.4032.4432.5432.70328232.9032.9833.0433.1433.2833.4333.5533.6433.6933.6933.6933.6933.7033.8834.1434.2834.44

25.9926.0026.0226.1226.2826.4026.4526.5126.5926.7026.8226.9327.0227.1027.1427.1427.1427.1427.1427.2627.3927.5027.71

TABLE 2Bj=+> e Before Mixing After Mixi ng

Layer


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24/42

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25/42

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29/42

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BIBLIOGRAPHY

BROWN, A. L. An analytical method of ice potential calculation.U. . Hydrographic Office, Technical Report jjS. Washington.September 1954-* 13p.DEFANT, A. Konvektion und Eisbereitschaft in polaren Schelfmeeren(Convection and ice formation in polar shelf seas), GeoerafiskaAnnaler . Arg. 31, pp. 25-35, 1949.JACOBS, W. C. On the energy exchange between sea and atmosphere,Journal of Marine Research . Vol. 5, pp. 37-66, 1942.ZUBOV, N. N. Morskie vody i l'dy (Marine water and ice). MoskvaGidrometeorologicheskoe Izdatel'stvo, 1938. 451p.

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Ice

FOceonogri Meteorolo

Sea

Ice

P o o_ '~ -iI to ^."Hu c ^ x -o E *S ? - i; 5 SSoo xSO-LLOIUffl s

aH-oc dX

U-i-Oq. ^ o Q_ _ Z ôog, u ra ON - T>iovinN

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iJ , TjOÔ^-olc * r U ?-%r-t/>U = i o o i * =, "c 3 c E o e n.2--. ."5-i'?- a vi *- r ~ x* r- ., - ? a-o o-o o c o o -

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2-- C3 a

dr.r-d

cv co tj ut >o rs.

S.

Navy

Hydrogrophic

Office

A

PRACTICAL

METHOD

OF

PREDICTING

SEA

E

FORMATION

AND

GROWTH,

by

Owen

S.

Lee

and

3ydS.

Simpson,

September

1954.

9p.,

4charts,

tables.

(H.

0.

TR-4).

1 : i i-S-2oic >--*_-5=ir.s 8 Be 01c 3 f c o e ooJ! c.S-o.= ? "> " x ~.tUill* S si., c * 8 oS -o o 'iii: gi? e 5 u u o S - > '- * --o e o c o e u

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sg1xâ S-Toi c .o m '5, ur 3 f E O Bfi*" " Ol '

? - e "" t 5 u o o -:~ ?"S--2'5~a o c c - '^ ora oi a 2 a>- = E o -o - z 5 >e X 3


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a practical method of predicting sea ice formation and growth (1954)

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