460ICEINTHESEAness of over 4 meters in this manner, or when summer melthaveshownthatthemost influential parametersaffectingseawaterfromitssurfaceorfromsnowcoverrunsoffintotheseaice growth are air temperature, wind speed, snowdepth andand refreezes under the ice where the seawater temperature isinitial ice thickness. Many complex equations have been for-belowthefreezingpointofthefreshermelt water.mulated to predict icegrowth using thesefour parametersThe growth of sea ice is dependent upon a number ofHowever,except for thefirst two, these parameters are notmeteorologicalandoceanographicparameters.Suchparam-routinely observed for remotepolar locations.eters include air temperature,initial ice thickness, snowField measurements suggest that reasonable growthdepth, wind speed, seawater salinity and density,and the spe-cific heats of sea ice and seawater.Investigations,however,estimatescanbeobtainedfromairtemperaturedataaloneLAAUNEJULYOaEAYeanE宇啤帘-25SteWS04500SANC4000320-30002500a200015001000500AUGSEPTOCTCECNOVFEB190S会181504013020(ao)116SEt0090301aR60503020Figure34o4a.RelationshipbetweenaccumulatedfrostdegreedaysandtheoreticalicethicknessatPointBarrow,Alaska
460 ICE IN THE SEA ness of over 4 meters in this manner, or when summer melt water from its surface or from snow cover runs off into the sea and refreezes under the ice where the seawater temperature is below the freezing point of the fresher melt water. The growth of sea ice is dependent upon a number of meteorological and oceanographic parameters. Such parameters include air temperature, initial ice thickness, snow depth, wind speed, seawater salinity and density, and the specific heats of sea ice and seawater. Investigations, however, have shown that the most influential parameters affecting sea ice growth are air temperature, wind speed, snow depth and initial ice thickness. Many complex equations have been formulated to predict ice growth using these four parameters. However, except for the first two, these parameters are not routinely observed for remote polar locations. Field measurements suggest that reasonable growth estimates can be obtained from air temperature data alone. Figure 3404a. Relationship between accumulated frost degree days and theoretical ice thickness at Point Barrow, Alaska
461ICEINTHESEA30025015型-1111111115,0006,0007,0008,0009.0001,0002.0003.004,00010,000ADCUMURCECREEDAYS(O'CBAEETEDFROSTEFigure 3404b. Relationship between accumlated frost degree days (°C) and ice thickness (cm).Various empirical formulae have been developed based onwhen temperatures remain below freezing. The relationshipthis premise.All appear to perform better under thin ice con-between frost degree day accumulations and theoretical iceditions when the temperature gradient through the ice isgrowth curvesatPointBarrow,Alaska isshown inFigurelinear, generally true for ice less than 100 centimeters thick3404a.Similar curves for otherArctic stations are containedDifferencesinpredictedthicknessesbetweenmodelsgener-inpublications availablefromtheU.S.NavalOceanographicallyreflect differencesin environmental1parametersOfficeandtheNationalIceCenter.Figure3404bgraphically(snowfal, heat content of the underlying water column, etc.)depicts the relationship between accumulated frost degreeat the measurement site.As a result, suchequations must beconsidered partially site specific and their general use ap-days (°C)and ice thickness in centimetersproached with caution.For example,applying an equationDuring winter, the ice usually becomes covered withderived from central Arctic data to coastal conditionsortosnow,which insulates the ice beneath and tends to slowAntarcticconditionscouldlead tosubstantial errors.Forthisdown its rateofgrowth.This thickness of snowcover variesreasonZubov's formula is widely cited as it represents an av-considerably from region to region as a result of differingerageofmanyyearsofobservationsfromtheRussianArctic:climatic conditions.Its depth may also vary widely withinh+50h=80very short distances inresponse to variable winds and ice to-pography. While this snow cover persists, about 80 to 85where h is the ice thickness in centimeters for agiven dayandpercent of the incoming radiation is reflected back to space. is the cumulative number of frost degreedays indegreesEventuallyhowever,the snowbeginstomelt,as theairtem-Celsius since the beginning of thefreezing seasonperaturerises above o°C inearly summer and the resultingAfrost degree day is defined as a day with a mean tem-freshwater forms puddles on the surface. These puddles ab-perature of obelow anarbitrarybase.The base mostsorbabout90percentof the incomingradiation and rapidlycommonly used is the freezing point of freshwater (O°C).If,for example, the mean temperature on a given day is 5°be-enlarge as they meltthe surrounding snow or ice.Eventuallylowfreezing,then fivefrostdegree days arenoted for thatthe puddles penetratetothebottom surfaceof the floes andday.Thesefrost degree days are then added to those noted theas thawholes. This slow process is characteristic of ice innextdaytoobtainan accumulatedvalue,whichisthenaddedthe Arctic Ocean and seas wheremovement is restricted byto those noted the following day.This process is repeatedthe coastline or islands.Where ice is free to drift into warmerdaily throughout the ice growing season.Temperatures usu-waters (e.g.,the Antarctic, EastGreenland,and theLabradorallyfluctuateaboveandbelowfreezingfor several daysSea),decay isaccelerated in responseto wave erosionasbefore remainingbelowfreezing.Therefore,frostdegreedayaccumulations areinitiated on the firstday of the periodwell as warmerairand seatemperatures
ICE IN THE SEA 461 Various empirical formulae have been developed based on this premise. All appear to perform better under thin ice conditions when the temperature gradient through the ice is linear, generally true for ice less than 100 centimeters thick. Differences in predicted thicknesses between models generally reflect differences in environmental parameters (snowfall, heat content of the underlying water column, etc.) at the measurement site. As a result, such equations must be considered partially site specific and their general use approached with caution. For example, applying an equation derived from central Arctic data to coastal conditions or to Antarctic conditions could lead to substantial errors. For this reason Zubov’s formula is widely cited as it represents an average of many years of observations from the Russian Arctic: where h is the ice thickness in centimeters for a given day and φ is the cumulative number of frost degree days in degrees Celsius since the beginning of the freezing season. A frost degree day is defined as a day with a mean temperature of 1° below an arbitrary base. The base most commonly used is the freezing point of freshwater (0°C). If, for example, the mean temperature on a given day is 5° below freezing, then five frost degree days are noted for that day. These frost degree days are then added to those noted the next day to obtain an accumulated value, which is then added to those noted the following day. This process is repeated daily throughout the ice growing season. Temperatures usually fluctuate above and below freezing for several days before remaining below freezing. Therefore, frost degree day accumulations are initiated on the first day of the period when temperatures remain below freezing. The relationship between frost degree day accumulations and theoretical ice growth curves at Point Barrow, Alaska is shown in Figure 3404a. Similar curves for other Arctic stations are contained in publications available from the U.S. Naval Oceanographic Office and the National Ice Center. Figure 3404b graphically depicts the relationship between accumulated frost degree days (°C) and ice thickness in centimeters. During winter, the ice usually becomes covered with snow, which insulates the ice beneath and tends to slow down its rate of growth. This thickness of snow cover varies considerably from region to region as a result of differing climatic conditions. Its depth may also vary widely within very short distances in response to variable winds and ice topography. While this snow cover persists, about 80 to 85 percent of the incoming radiation is reflected back to space. Eventually, however, the snow begins to melt, as the air temperature rises above 0°C in early summer and the resulting freshwater forms puddles on the surface. These puddles absorb about 90 percent of the incoming radiation and rapidly enlarge as they melt the surrounding snow or ice. Eventually the puddles penetrate to the bottom surface of the floes and as thawholes. This slow process is characteristic of ice in the Arctic Ocean and seas where movement is restricted by the coastline or islands. Where ice is free to drift into warmer waters (e.g., the Antarctic, East Greenland, and the Labrador Sea), decay is accelerated in response to wave erosion as well as warmer air and sea temperatures. Figure 3404b. Relationship between accumlated frost degree days (°C) and ice thickness (cm). h 2 + 8 50h = ∅
462ICEINTHESEA3405.SalinityOf Sea Icesity of the water in which it floats. Thus, if an iceberg ofdensity0.920floats inwaterofdensity1.028(correspondingto a salinityof35parts per thousand and a temperatureofSea ice forms first as salt-free crystals near the surface-1°C),89.5 percent of its mass will be below the surface.ofthesea.Astheprocesscontinues,thesecrvstalsarejoinedtogether and, as they do so, small quantities of brine areThe height to draft ratio for a blocky or tabular icebergtrapped withintheice.Onthe average,new ice15 centime-probablyvariesfairlycloselyabout 1:5.This averageratio wasters thick contains 5to10 parts of saltper thousand.Withcomputed for icebergs south of Newfoundland by consideringlowertemperatures,freezingtakesplacefaster.Withfasterdensityvalues andafewactual measurements,andbyseismicfreezing,agreateramountof salt is trapped inthe ice.meansatanumberoflocationsalongtheedgeoftheRossIceShelf near LittleAmerica Station.It was also substantiated byDepending upon the temperature, the trapped brine may eidensity measurements taken in a nearbyholedrilled throughtherfreeze or remain liquid,but because its densityis greaterthe 256-meter thick ice shelf. The height to draft ratios of ice-than that of the pure ice, it tends to settle down through the purebergs become significant when determining their drift.ice.As it does so, the icegradually freshens, becoming clearer,stronger, and more brittle. At an age of1 year, sea ice is suff-cientlyfreshthat itsmeltwater, iffound inpuddlesofsufficient3407.DriftOfSeaIcesize.andnotcontaminatedbysprayfromthesea.canbeusedtoreplenish the freshwater supply of a ship. However, ponds ofAlthough surface currents have some affect upon thesufficientsizetowatershipsareseldomfoundexceptiniceofdriftof packice,theprincipalfactoriswind.Dueto Corio-great age, and then much of the meltwater is from snow whichlis force,ice doesnotdrift in the direction of the wind, buthas accumulated onthesurfaceofthe ice.When seaicereachesvariesfromapproximately18toasmuchas 90ofromthisanageofabout2vearsvirtuallyallofthesalthasbeeneliminat-direction,depending upontheforceofthe surfacewindanded.Icebergs,havingformed from precipitation,containno salt,theicethickness.IntheNorthernHemisphere,thisdriftisanduncontaminatedmeltwaterobtainedfromthemisfreshto the right of the direction toward which thewind blows.The settling out of the brinegives sea ice a honeycomband in the Southern Hemisphere it is toward the left.Al-structure which greatly hastens its disintegration when thethough earlyinvestigators computed average angles oftemperaturerises abovefreezing.In this state,when itisapproximately 280or290for the drift of close multiyearcalledrottenice,muchmoresurface isexposedtowarmairpack ice,large drift angles were usually observed withlowandwater,andtherateofmeltingisincreased.Inaday'srather than high, wind speeds.The relationship betweentime,afloeofapparentlysolid ice several inchesthick maysurface wind speed, ice thickness, and drift angle was de-disappearcompletely.rived theoreticallyforthe drift of consolidated pack underequilibrium(abalanceofforcesactingontheice)condi-3406.DensityOf Icetions, and shows that the drift angle increases withincreasing icethickness and decreasing surface wind speedA slight increase also occurs with higher latitude.The density of freshwater ice at its freezing point is0.917gm/cm3.Newlyformed sea ice,due to its saltcontent,Sincethecross-isobar deflection of the surfacewindismoredense,0.925gm/cm3beinga representativevalueovertheoceans is approximately20°,thedeflection of theThe densitydecreases as the icefreshens.Bythe time it hasicevaries,fromapproximatelyalong the isobarstoasmuchshedmostofitssalt.seaiceislessdensethanfreshwateras7oototherightoftheisobars,withlowpressureontheice, because ice formed in the sea contains more air bub-left and high pressure onthe right in the Northern Hemi-bles.Icehavingnosaltbutcontainingairtotheextentof8sphere.The positions of the low and high pressure areas are,percentbyvolume(an approximatelymaximumvalueforof course,reversed in the Southern Hemisphere.seaice)hasadensityof0.845gm/cm3Therateof drift depends upon the roughness of theThe density of land icevaries over even wider limitssurface and the concentration of the ice. PercentagesThat formed by freezing of freshwaterhas a densityofvaryfromapproximately0.25percenttoalmost8per-0.917gm/cm3,asstatedabove.Muchofthelandice,howev-cent of thesurfacewindspeedasmeasureder, is formed by compacting of snow. This results in theapproximately 6 meters above the ice surface.Low con-entrappingofrelativelylarge quantities ofair.Neve,a snowcentrations of heavily ridged or hummocked floes driftwhichhasbecomecoarsegrainedandcompactthroughtem-fasterthanhighconcentrationsoflightlyridgedorhum-peraturechange,forming the transition stage to glacier icemockedfloeswith the samewind speed.Sea ice of 8tomayhaveanaircontentofasmuchas50percentbyvolume9 tenths concentrations and sixtenths hummockingorBy the time the ice of a glacier reaches the sea, its densityclose multiyear ice will drift at approximately2 percentapproachesthatoffreshwaterice.Asampletakenfromanof the surfacewind speed.Additionally,the responseicebergontheGrandBankshadadensityof0.899gm/cm3.factorsof1and5tenths ice concentrations,respectively,Whenicefloats,partofitisabovewaterandpartisbelowareapproximatelythreetimes and twicethemagnitudethesurface.Thepercentageofthemass belowthesurfacecanoftheresponsefactorfor9tenthsiceconcentrationswithbefound bydividingthe averagedensity oftheicebythe den-the same extent of surface roughness.Isolated icefloes
462 ICE IN THE SEA 3405. Salinity Of Sea Ice Sea ice forms first as salt-free crystals near the surface of the sea. As the process continues, these crystals are joined together and, as they do so, small quantities of brine are trapped within the ice. On the average, new ice 15 centimeters thick contains 5 to 10 parts of salt per thousand. With lower temperatures, freezing takes place faster. With faster freezing, a greater amount of salt is trapped in the ice. Depending upon the temperature, the trapped brine may either freeze or remain liquid, but because its density is greater than that of the pure ice, it tends to settle down through the pure ice. As it does so, the ice gradually freshens, becoming clearer, stronger, and more brittle. At an age of 1 year, sea ice is sufficiently fresh that its melt water, if found in puddles of sufficient size, and not contaminated by spray from the sea, can be used to replenish the freshwater supply of a ship. However, ponds of sufficient size to water ships are seldom found except in ice of great age, and then much of the meltwater is from snow which has accumulated on the surface of the ice. When sea ice reaches an age of about 2 years, virtually all of the salt has been eliminated. Icebergs, having formed from precipitation, contain no salt, and uncontaminated melt water obtained from them is fresh. The settling out of the brine gives sea ice a honeycomb structure which greatly hastens its disintegration when the temperature rises above freezing. In this state, when it is called rotten ice, much more surface is exposed to warm air and water, and the rate of melting is increased. In a day’s time, a floe of apparently solid ice several inches thick may disappear completely. 3406. Density Of Ice The density of freshwater ice at its freezing point is 0.917gm/cm3. Newly formed sea ice, due to its salt content, is more dense, 0.925 gm/cm3 being a representative value. The density decreases as the ice freshens. By the time it has shed most of its salt, sea ice is less dense than freshwater ice, because ice formed in the sea contains more air bubbles. Ice having no salt but containing air to the extent of 8 percent by volume (an approximately maximum value for sea ice) has a density of 0.845 gm/cm3. The density of land ice varies over even wider limits. That formed by freezing of freshwater has a density of 0.917gm/cm3, as stated above. Much of the land ice, however, is formed by compacting of snow. This results in the entrapping of relatively large quantities of air. Névé, a snow which has become coarse grained and compact through temperature change, forming the transition stage to glacier ice, may have an air content of as much as 50 percent by volume. By the time the ice of a glacier reaches the sea, its density approaches that of freshwater ice. A sample taken from an iceberg on the Grand Banks had a density of 0.899gm/cm3. When ice floats, part of it is above water and part is below the surface. The percentage of the mass below the surface can be found by dividing the average density of the ice by the density of the water in which it floats. Thus, if an iceberg of density 0.920 floats in water of density 1.028 (corresponding to a salinity of 35 parts per thousand and a temperature of –1°C), 89.5 percent of its mass will be below the surface. The height to draft ratio for a blocky or tabular iceberg probably varies fairly closely about 1:5. This average ratio was computed for icebergs south of Newfoundland by considering density values and a few actual measurements, and by seismic means at a number of locations along the edge of the Ross Ice Shelf near Little America Station. It was also substantiated by density measurements taken in a nearby hole drilled through the 256-meter thick ice shelf. The height to draft ratios of icebergs become significant when determining their drift. 3407. Drift Of Sea Ice Although surface currents have some affect upon the drift of pack ice, the principal factor is wind. Due to Coriolis force, ice does not drift in the direction of the wind, but varies from approximately 18° to as much as 90° from this direction, depending upon the force of the surface wind and the ice thickness. In the Northern Hemisphere, this drift is to the right of the direction toward which the wind blows, and in the Southern Hemisphere it is toward the left. Although early investigators computed average angles of approximately 28° or 29° for the drift of close multiyear pack ice, large drift angles were usually observed with low, rather than high, wind speeds. The relationship between surface wind speed, ice thickness, and drift angle was derived theoretically for the drift of consolidated pack under equilibrium (a balance of forces acting on the ice) conditions, and shows that the drift angle increases with increasing ice thickness and decreasing surface wind speed. A slight increase also occurs with higher latitude. Since the cross-isobar deflection of the surface wind over the oceans is approximately 20°, the deflection of the ice varies, from approximately along the isobars to as much as 70° to the right of the isobars, with low pressure on the left and high pressure on the right in the Northern Hemisphere. The positions of the low and high pressure areas are, of course, reversed in the Southern Hemisphere. The rate of drift depends upon the roughness of the surface and the concentration of the ice. Percentages vary from approximately 0.25 percent to almost 8 percent of the surface wind speed as measured approximately 6 meters above the ice surface. Low concentrations of heavily ridged or hummocked floes drift faster than high concentrations of lightly ridged or hummocked floes with the same wind speed. Sea ice of 8 to 9 tenths concentrations and six tenths hummocking or close multiyear ice will drift at approximately 2 percent of the surface wind speed. Additionally, the response factors of 1 and 5 tenths ice concentrations, respectively, are approximately three times and twice the magnitude of the response factor for 9 tenths ice concentrations with the same extent of surface roughness. Isolated ice floes
463ICEINTHESEA903085650080ASSUNPTION-EGUILIBRUNCONDITIONST5ANDS/BICECONCENTRATION000COMPUTED FOR 66*SO'LATITUDE70AFTERSHULEIKIN,I9SS(MOOIFIED)6scoLie'0ssICETHICKNESS CURVES505o(FEET)*34340403s3330305252020.1501On-40505220222426283032343638O1610041SURFACE WIND SPCED [KNOTS)Figure3407.Ice drift directionforvarying wind speed and ice thicknesshavebeen observed todrift as fast as 10percent to12per-riety of factors such as horizontal pressure gradients owingcentof strong surface winds.to density variations in the water, rotation ofthe earth,grav-itationalattractionofthemoon,and slopeofthe sea surface.The rates at which sea ice drifts have been quantifiedWind not only acts directly on an iceberg,but also indirect-through empirical observation, The drift angle, however,ly by generating waves and a surface current in about thehasbeendeterminedtheoreticallyfor10 tenths ice concen-same direction as the wind.Because of inertia, an icebergtration.This relationshippresentlyisextendedtothedriftofmay continuetomovefrom the influence ofwind for someall iceconcentrations,duetothelackofbasicknowledgeoftimeafterthe wind stops orchangesdirection.thedynamicforces thatactupon,andresult inredistributionof seaice, inthepolar regions.The relative influence of currents and winds on thedriftof an iceberg varies according to the direction and magnitude3408. Iceberg Driftof theforces acting on its sail areaand subsurface cross-sec-tional areaThe resultant force therefore involves theproportions ofthe iceberg above and below the sea surface inIcebergs extend a considerable distance below the sur-relation to the velocity and depth of the current, and the ve-face andhave relatively small sail areas"compared to theirlocityanddurationofthewind.Studiestendtoshowthat.subsurface mass.Therefore, the near-surface current isgenerally,wherestrong currents prevail,thecurrent is domi-thoughttobeprimarily responsiblefordrift; however, ob-nant. In regions of weak currents,however,winds that blowservations have shown that wind canbe thedominant forcefora number of hours ina steady direction materially affectthat governs iceberg drift at a particular location or time.the drift of icebergs.Generally, it can be stated that currentsAlso, the current and wind may contribute nearly equally totend to have a greater effect on deep-draft icebergs, whiletheresultantdriftwinds tend to have a greater effect on shallow-draft icebergs.Two other major forces which act on a drifting icebergAs icebergs waste through melting, erosion, and calv-are the Coriolis force and, to a lesser extent, the pressureing, observations indicate the height to draff ratio maygradient force which is caused by gravity owing to a tilt ofthe sea surface, and is important only for iceberg drift in aapproachl:1 during theirlast stageof decay,when they aremajor current. Near-surface currents are generated by a va-referred to as valley, winged, horned, or spired icebergs
ICE IN THE SEA 463 have been observed to drift as fast as 10 percent to 12 percent of strong surface winds. The rates at which sea ice drifts have been quantified through empirical observation. The drift angle, however, has been determined theoretically for 10 tenths ice concentration. This relationship presently is extended to the drift of all ice concentrations, due to the lack of basic knowledge of the dynamic forces that act upon, and result in redistribution of sea ice, in the polar regions. 3408. Iceberg Drift Icebergs extend a considerable distance below the surface and have relatively small “sail areas” compared to their subsurface mass. Therefore, the near-surface current is thought to be primarily responsible for drift; however, observations have shown that wind can be the dominant force that governs iceberg drift at a particular location or time. Also, the current and wind may contribute nearly equally to the resultant drift. Two other major forces which act on a drifting iceberg are the Coriolis force and, to a lesser extent, the pressure gradient force which is caused by gravity owing to a tilt of the sea surface, and is important only for iceberg drift in a major current. Near-surface currents are generated by a variety of factors such as horizontal pressure gradients owing to density variations in the water, rotation of the earth, gravitational attraction of the moon, and slope of the sea surface. Wind not only acts directly on an iceberg, but also indirectly by generating waves and a surface current in about the same direction as the wind. Because of inertia, an iceberg may continue to move from the influence of wind for some time after the wind stops or changes direction. The relative influence of currents and winds on the drift of an iceberg varies according to the direction and magnitude of the forces acting on its sail area and subsurface cross-sectional area. The resultant force therefore involves the proportions of the iceberg above and below the sea surface in relation to the velocity and depth of the current, and the velocity and duration of the wind. Studies tend to show that, generally, where strong currents prevail, the current is dominant. In regions of weak currents, however, winds that blow for a number of hours in a steady direction materially affect the drift of icebergs. Generally, it can be stated that currents tend to have a greater effect on deep-draft icebergs, while winds tend to have a greater effect on shallow-draft icebergs. As icebergs waste through melting, erosion, and calving, observations indicate the height to draft ratio may approach 1:1 during their last stage of decay, when they are referred to as valley, winged, horned, or spired icebergs. Figure 3407. Ice drift direction for varying wind speed and ice thickness