459
1 BACKGROUND
Since the sinking of the passenger ship Titanic in
1912,theInternationalIcePatrol(IIP)haskeptwatch
in waters off Newfoundland, south of 48N latitude
and east to about 40 west longitude. Here icebergs
threaten off‐shore oil rigs, fishing boats and
commercialshipsontheirway
toEuropeandAfrica.
In this work we investigate the effects of climate
changeonicebergsintheNWAtlantic.Increasingsea
surface temperatures, decreasing current velocities,
windsandsea‐icewillbeshowntohaveasignificant
effectonthemeltingoficebergs.
Greenland’s sea/glacier interfaces are the main
source of icebergs floating into the NW Atlantic
shipping lanes off Newfoundland. These icebergs
typically move northward with the West Greenland
Currentaftercalving,thensouthalongtheLabrador
and Baffin Island coasts until reaching the shipping
lanesatthe48
th
paralleloffNewfoundland–a3000to
4000 km journey that can take years to complete
(Canadian Coast Guard, 2012). Figure 1 shows the
normal iceberg trajectories, as well as the major
Greenland calving locations. For scale, the distance
from the southern tip of Greenland to the northern
endof
BaffinBayisaboutthesameasfromFloridato
NewYork,U.S.A.
Icebergdriftstudies byMarkoet al. (1982),Robe
andMaier(1979),Robe etal.(1980)followedicebergs
fromtheeastcoastofBaffinIslanddowntoasfaras
48 N latitude near Newfoundland.Of all the
icebergs tracked, only two came close to 48N –
Iceberg Melting and Climate Change in NW Atlantic
Waters
S.E.Perez‐Gruszkiewicz&W.Peterson
U.S.MerchantMarineAcademy,KingsPoint,NY,USA
ABSTRACT: Climate change is predicted to cause increases in sea surface temperature (SST), as well as
decreases insea‐icecover,windand current velocities. These changes will have a marked effect on iceberg
meltingintheshippinglanesoffNewfoundlandandLabrador,
Canada.
IcebergsthattodaycancrossfromnorthernLabradortoNewfoundlandwithoutmeltingwillinthefuturehave
tobe muchlarger to survivethe transit. For example, icebergs at N Labrador inDecember of 2016 that are
smallerthan156mwillmeltbeforereaching48N,butinyear
2100thelengthincreasesto228m.Inaddition,if
future iceberg size distributions off Labrador are the same as toda y, icebergs will experience roughly 50%
reductionsinnumbersintheNWAtlanticshippinglanesbyyear2100.
Theincreasedmeltingratesaredueto,inorderofimportance,increasedsea
‐surfacetemperatures(responsible
for66%oftheincreaseintheminimumtransitsize),decreasingcurrentvelocities(31%),anddecreasingsea‐ice
cover(3%).Decreasingsea‐icetendstoincreasewaveheightsaswellasacceleratetheeffectsofwaveerosion;
however,fortheareasstudiedthewaveheightispredicted
todecreasemoderatelyinyear2100,byamaximum
ofabout10%inDecember.
http://www.transnav.eu
the International Journal
on Marine Navigation
and Safety of Sea Transportation
Volume 12
Number 3
September 2018
DOI:10.12716/1001.12.03.04
460
icebergsnumber160and344(RobeandMaier(1979)
andRobeetal.(1980)).Asfarasweknowthesetwo
bergs had the longest observed runs of any iceberg
trackedintheNWAtlantic,from67Ndowntoabout
48N,atroughly150kmfromshore.
Figure1. Track followed by icebergs after calving. Image
fromCanadianCoastGuard(2012).
Only a small portion of icebergs calved in
Greenland are estimated to make it to the shipping
lanes south of the 48
th
parallel, succumbing to
prolonged groundings and eventual melting. No
iceberg has ever been followed from its birth to the
shipping lanes. In Nalcor ( 2015), the authors
documentthatmorethan90%oftheicebergsdrifting
south from northern Labrador to 48N do so within
about6degreesoflongitude
oftheshore,adistance
ofroughly360km.
There is great year‐to‐year variability in the
numbersoficebergsdriftingintotheshipping lanes.
Yearlyicebergnumberscanrangefromnonetomore
than 2000. Peterson et al. (2000) and Marko (1984)
found that sea‐ice extent was the
most important
factorincorrelatingicebergseasonalvariability.Wind
direction has also been shown to be important, as
easterlywindstendtomoveicebergstowardsshore.
The prevailing wind direction however is from the
WNW(Nalcor,2015).Petersonetal.(2000)andIIP
(2015)studiedtheeffectoftheNAO
(NorthAtlantic
Oscillation).TheyfoundastronglinkbetweenNAO
indexandicebergtotals.Newell(1991)proposedthat
variability in yearly iceberg numbers may be
influenced by the break‐up of huge ice islands that
periodically drift into the waters off Labrador and
Newfoundland. Bigg et al. (2014) proposed that
yearly
variabilityinicebergnumbersintheshipping
lanesmaybecausedbyvariabilityinicebergcalving
atglaciertermini.
White et al. (1980) conducted a review of ice
melting literature as well as wave erosion
experiments in a tank.They used these data with
dimensionalanalysistodevelopequationsfor
iceberg
wave erosion, forced convection, and the failure
lengthofoverhanging slabs thatarecutintoiceberg
surfacesbywaveerosion.Theseslabsresultincalving
when they reach the failure length, but the failure
lengthequationofWhiteetal.requiresknowledgeof
the overhanging slab thickness, which was beyond
the scope of the work by White et al. Savage (1999)
developed an equation for the thickness of
overhanging slabs, permitting relatively simple
iceberg calving calculations using White’s equation.
EL‐Tahan et al. (1987) used observations of icebergs
off Labrador and the Grand Banks to test White’s
methods, considering buoyancy‐
driven (natural)
convection, water forced convection, wave erosion,
and calving (it is unclear from their paper how the
thickness of the overhanging slab was calculated).
The authors found the parametrizations outlined in
White et al. (1980) resulted in good agreement with
observed data. EL‐Tahan also found that neither
insolation nor
air/iceberg heat transfer play a
significantroleinNWAtlanticicebergmelting.
SinceWhite’spaperwaspublished,someformof
hisequationshavebeenadoptedbytheInternational
IcePatrolandtheCanadianIceServiceforpredicting
iceberg drift and deterioration. To reduce
computational time, simplified equations for iceberg
melting
have been used by Bigg (1997, 1996) and
Wagner (2017) to model long‐range drifts of large
numbers of icebergs. In particular, wave erosion
predictions were made a function of the sea state
only,independentofSST(seasurfacetemperature).
Hanetal.(2015)usedGlobalandRegionalClimate
Models (GCMs
and RCMs) to predict reductions in
iceberg numbers due to climate change. They
extrapolatedacorrelationbetweenairtemperatureat
Labrador and icebergs below 48N to the climate‐
model‐predicted air temperatures, in order to
determine future iceberg numbers in the shipping
lanes.Theauthorsusedaconservativeassumptionfor
CO2 emissions (Representative Concentration
Pathway 4.5 (RCP4.5) as well as a more aggressive
emissionsscenario(RCP8.5).Theauthorsfoundthat,
relative to the 813 iceberg mean from 1981‐2010,
icebergsbelow48Nwoulddecreaseby30%to100%
bytheyear2060.
CESM1‐CAM5 is thehighest‐rated climate model
by
Knutti et. al (2013). The authors evaluated 38
models from World Climate Research Programme
Coupled Model Intercomparison Project Phase 5
(CMIP5).
RCP8.5 is an acronym for Representative
Concentration Pathway, a future greenhouse gas
emission scenario sometimes referred to as a
“business as usual” model. In RCP8.5, emissions
continuetorise
toa CO2concentrationof about940
ppm. Actual greenhouse gas emissions have most
461
closely matched RCP8.5 of all the scenarios tested
(Alexanderetal.,2018).
In this work we use predictions from climate
models with the RCP8.5 emission scenario to
determine what effect changing environmental
parameters will have on the melting of icebergs off
Newfoundland and Labrador, and to estimate
changes in future
iceberg numbers drifting into the
NWAtlanticshippinglanes.
2 METHODS
2.1 General
Asmentionedearlier,icebergscantakeyearstocover
the distance from calving sites to shipping lanes.
Icebergshavenotbeenfollowedover the entiretyof
theirjourney,andthusimportantdetailssuchasdrift
velocities,paths
followedandgroundingfrequencies
areunknown.
Due to this paucity of information, we consider
only future iceberg melting from northern Labrador
toNewfoundland.Thisisa geographicalareathathas
beenthoroughlystudiedbytheoilandgasindustry.
Nalcor (2015) presents historical averages of winds,
currents, ice cover, wave heights,
ship icing, sea
temperatures,icebergsandvisibilityoffLabradorand
Newfoundland.
Ouranalysis is based on what can be considered
an average iceberg path off Labrador and
Newfoundland, between 60N and 48N, at about 2.5
degrees longitude off‐shore (a distance ofabout 150
km),alongapathsimilarto
Robe’sicebergs160and
344.Nalcor(2015)foundthatgreaterthan90%ofthe
icebergs drifting south along Labrador and
Newfoundlandshoresdosowithinabout5degreeof
longitudeoff‐shore,onaverage.
Thedistanceoff ‐shorehasaveryimportanteffect
on iceberg melting rates. Icebergs within about 1
degree longitude may experience very slow drift
velocities, sometimes in directions opposing the
normal north‐south movement of the Labrador
current (Nalcor 2015). In addition, sea‐surface
temperatures are considerably warmer off‐shore,
where the influence of the warm northerly flowing
North‐Atlantic current is more pronounced. The
extent of
sea‐ice cover is also greatest near‐shore,
which tends to protect icebergs by decreasing wave
heightsaswellasprotectingthemfromtheeffectsof
wave erosion. Waves tend to be larger off‐shore,
alongwithhigherwindspeeds.
Theresultisthat,assumingequaldriftvelocities,
icebergsaremore
protectedfrommeltingwhenthey
areclosertoshore.Buttherealitymaybethatthese
icebergs are much less likely to survive the journey
due to groundings and excessive exposure time.
Initiallyitwasourgoaltoanalyzeicebergmeltingfor
paths close to shore (icebergs within 1 degree
of
longitude to Labrador and Newfoundland shores
constituteabout10percentofallbergsmovingsouth)
as well as off‐shore, but such an effort would be
plagued by too much uncertainty in transit times
from 60N to 48N. More iceberg observations are
required.
Ourschemeinvolvesallowingicebergs todrift
in
one‐dayincrements(ortimesteps)beginningat60N,
andthenusingameltingmodeltodetermineiceberg
size at the end of the time step. The melting model
requires input of environmental parameters such as
SST, ice fraction and wind speed. These were
averaged over an area encompassing
Labrador and
Newfoundland shores out to about 5 degrees of
longitudefromtheshore,asafunctionofthemonth,
and parametrized in trendlines. Wave heights are
calculated at each time steps using relations we
derived, as a function of wind speed and sea‐ice
coverage.Inthefollowingsectionswe
providefurther
details dealing with environmental parameters as
wellasourmeltingmodel.
2.2 Climatedata
Climate model CESM1‐CAM5 results were
downloadedfromtheCenterforEnvironmentalData
Analysiswebsite(NCAR,2017),andusedtoestimate
futureaveragesea‐surfacetemperature(SST),winds,
y‐component current velocities (north to
south) and
sea‐ice coverage in Labrador and Newfoundland
waters.Thesewereaveragedintheareabetweenthe
shoreline and about 6 longitude degrees east of the
shore. Trends were averaged monthly, over 20‐year
periodsbetween2006and2025(referredtoasCESM1
year 2016 average), and between 2081 and
2100
(referredtoasCESM1futureoryear2100averages).
Wind trends were determined over 15 year‐periods
(2006‐2020, and 2086‐2100), as these had a much
smalleryear‐to‐yearvariance.
Climate model results were downloaded and
analyzed with a Linux version of Panoply (NASA
GISS,2018).
We
refertothedifferencebetweenCESM1future
and CESM1 current environmental values as the
CESM1anomalies.Thesewereaddedtoobserved20‐
year average parameters, calculated from
environmentaldatafromHadlSST(2003)inthesame
wayastheCESM1data,yieldingpredictedyear2100
environmental averages. HadlSST (2003) data
includespast
SST,icecoverandwinds.Waveheights
over the past 20 years were obtained from Nalcor
(2015).
Year2100DriftVelocitiesandCrossingTimes:We
firstconstructaplotofyear2016driftvelocityinthe
y‐directionasafunctionofthemonthbyplottingthe
velocitiesofRobe’s340and160icebergsonFigure2
(yellow squares), and then scaling the CESM1 year
2016plottothosepoints(Robe2016onFigure2).This
plotisthenmoveddownbythesameamountasthe
CESM1 2100‐2016 anomaly (the difference between
theCESM12016andCESM12100plotsonFigure2),
resulting in year 2100 predicted average drift
velocities in the y‐direction (dashed blue line on
Figure2).
Velocities for Robe’s 160
and 344 icebergs were
measuredin1977and1978,andweusedtheseassea‐
currentvelocitiesin2016forouranalysis.Wefeltthis
was justified, as applying the CESM1‐calculated
averagerate ofchange of current velocity from 2006
to2026tothe1977and1978observationsresultedin
a
462
relatively small changes in drift velocity between
1977/78and2016.
The drift time required to make the 1350 km
journey(distanceiny‐directionfrom60Nto48N)was
calculatedbynumericallyintegrating
intime
stepsof0.2daysuntil1350kmweretraversed,using
the“Robe2100”plotfromFigure2foryear2100and
the“Robe2016”plotforyear2016.
Figure 3 shows the crossing times (generated by
observed and calculated drift velocities) for years
2100and2016,from60N
to48Nlatitude,asafunction
of month initiating the crossing. The plot shows
increasesintransit timesranging from6 to 13days,
withthelargestincreasesinwintermonths.
Figure2.y‐directioncurrentvelocity.Thelower2linesare
the CESM1 year 2100 and year 2016 y‐direction velocities.
Thedifferencebetweenthesetwo(the CESM1anomaly)is
theamount bywhich theyear2016 y‐velocity(topline) is
reduced, resulting in the year 2100 average drift velocity
(bluedashedline).
Figure 3. Days to complete the transit from 60N to 48N
latitudealongatypicalicebergpathinyears2016and2100.
2.3 SeaSurfaceTemperature(SST)
CESM1predictsanincreasedseasurfacetemperature
(SST)in year 2100of 2.3to 0.75 degreesC. Figure4
showsthebiggestincreasesareinDecember,January,
JulyandAugust.
Figure4.Sea‐surfacetemperatures(SST)foryears2100and
2016,averagedinwatersoffLabradorandNewfoundland.
2.4 Sea‐IceCoverage
Figure5showsasignificantdecreaseinsea‐icecover
in the winter months by year 2100. This decrease
tendstoleadtoincreasedwaveheightsanddecreased
protection of icebergs by sea‐ice.But, as will be
shown in a later section, this difference is not
very
importantinoverallicebergmelting,asthemitigating
effects of ice fraction on wave height and wave
erosion are greatest above 85% ice cover, and
relativelysmallbelowthis.
Figure5. Sea‐ice percentage for years 2016 and 2100,
averagedinwatersoffNewfoundlandandLabrador.
2.5 Winds
Windscanmoveicebergsrelativetothesurrounding
water, causing forced convection heat transfer. In
addition,windsdirectlyaffectwaveheights.Figure6
shows a slight decrease in year 2100 wind speed,
averagedinwatersoffNewfoundlandandLabrador.
Figure6.WindspeedsoffNewfoundlandandLabradorfor
years2016and2100.
463
2.6 Waveheights
Equations for wave height as a function of wind
speed, icecoverage and fetchwere developed using
dimensional analysis and historical environmental
data.
Wave heights are known to depend on wind
speed,sea‐icecoverageandfetch.TheBuckinghampi
theorem (White, 2016) then dictates two
dimensionless
groups can describe wave height
results.Usingatrialanderrorprocesstheseequations
werefoundtobe:
fetch cos 1
*
wave ht
ice fraction
H
[1]
where H* can be considered a dimensionless wave
height,fetchisthedistanceoff‐shorealongaparallel
of latitude, ice fraction is the fraction of the sea
surfacethatiscoveredbysea‐ice,andwavehtisthe
waveheight,inthesame unitsasthefetch.
Also,we
defineadimensionlessfetchF*:
1
2
*9.8 ) 1 /
F
fetch cos ice fraction wind speed
[2]
We note that the 9.8 isthe gravitational constant
inm/s
2
.
Figure7showsaplotofH*asafunctionofF*.A
3
rd
degree polynomial trendline fits the wave data
fromNalcor(2015),foryears1954‐2013,fromwinter,
spring and summer seasons with R^2 value of 0.74,
from½degreeoflongitudeeastoftheshorelinetoan
average of 5 degrees (4 degrees east at 58‐60 N, 5
degrees from
52‐56N, and 7 degrees at 49N). This
ensuredcapturing greaterthan90%ofalltheicebergs
transiting south along Labrador and Newfoundland
shores(Nalcor,2015).
Figure7. Dimensionless wave height H*as a function of
dimensionless fetch F*. F* values between 40 and 100 are
within1degreeoflongitudefromtheshore.Theremaining
pointsareatavarietyoffetchvaluesfrom30to300km.The
dottedlineshowsthetrendline.
Thetrendlinegeneratedwas:
H*=‐0.045376F*
3
+13.820094F*
2
‐344.731632F* [4]
Thetrendlineachievesareasonablefittothedata,
asshowninFigure8below:
Figure8. Predicted and observed wave heights using
equations(1)‐(4).
The large absolute magnitude errors at
observationnumbersthataremultiplesof4areatthe
furthest fetch, corresponding to about 5 degrees of
longitudefromtheshore.
Figure 9 shows the wave heights at 2.5 degrees
fromshore, as well as at0.5 degrees, for years 2016
and 2100, using
our wave height relation with
predicted (2100) and observed (2016) environmental
data.Moderatedecreasesinwaveheightareseenin
year2100,duetowindspeedreductions.Reductions
inicecover,althoughlarge(forexample,inJanuary,
icecoverdropsfrom34%inyear2016to14%in2100),
occur
aticefractionsthatarelowenoughsoasnotto
causesignificantincreasesinwaveheight.
The near‐shore wave heights also merit
contemplation: wave heights in December, when
thereisverylittleicepresenttoday,showadecrease
in height in year 2100 due to reduced windspeeds.
However,
by January and beyond, when currently
significanticeispresent,thedecreaseinyear2100ice
coverresultsinincreasedwaveheights.
Figure9. 2016 and 2100 wave heights at 2.5 degrees
longitude(off‐shore)and½degree(near‐shore).
2.7 Icebergmeltingmodel
We used the iceberg melting model developed by
Whiteetal.(1980)withthecalvingmodelofSavage
(1999) and a wave‐erosion damping coefficient from
GladstoneandBigg(2001),todeterminemeltingrate
of icebergs, given wind speed, wave height, sea‐
surface temperature and ice fraction.
These
formulationsare documented in theliterature, but a
brief description of how they are used is presented
here.
464
Icebergs off Newfoundland and Labrador are
exposedtothreedominantmodesofheattransfer(El‐
Tahanetal.,1987).Theyare,inorderofimportance:
1 Convection/erosioncausedbywaveaction,which
causes½‐3/4ofallmelting.
2 A by‐product of wave erosion known as calving.
Wave action
causes a notch in the iceberg that
eventuallybecomeslargeenoughtobreakoffdue
to the weight of the ice overhanging the notch.
Calvingcausesapproximately¼ofallmelting.
3 Convectiveheattransferduetothemotionofthe
icebergrelative to the surrounding water, caused
bywind
actionandcurrentvariationswithdepth.
Theconvectiveheattransferaccountsforabout¼
ofallmelting.Thespeedoftheicebergrelativeto
thesurroundingwaterisdeterminedbyarelation
recommended by El‐Tahan and confirmed by
Wanger(2017)of0.017ofthewindspeed.
Otherfactorsinfluencingicebergmelting,
suchas
solarradiation, buoyant convection caused by water
density gradients, and convection on the air side of
the iceberg are small enough to be overlooked (EL‐
Tahanetal.,1987).
Themeltingmodelresultsinameltingratewhich
can be numerically integrated over time. We usean
explicit
scheme for marching forward in time, with
theicebergdimensionsof the previoustimestep for
allcalculations.Thisprocedurerequiresasufficiently
small time step, determined by a trial‐and‐error
process until the elapsed time to melt no longer
changessignificantly.1daywasdeterminedtobean
appropriate
timestepforthesecalculations.
The iceberg was assumed to be of the “blocky”
type,asdescribedbyRobe(1983),withequallength
and width, and a height that is 0.7 times the side
length.At the end of each time step, new mass and
dimensionsoftheicebergare
calculated,afterwhicha
newtimestepisbegun.Whenthema ssoftheiceberg
reacheszero,theiceberghasmeltedandtheiterations
finish.
Icebergsaresurroundedmostoftheyearbyfrozen
sea water of varying sea‐ice fraction (ice area/total
area), known as pack‐ice or sea‐ice
(in contrast,
icebergs are composed of frozen fresh‐water from
glacier termini). Sea‐ice can have a significant effect
onicebergmeltingfortworeasons:a)sea‐icelowers
the height of waves b) sea ‐ice provides damping of
theerodingeffectofwaves.
Weusedtheequationgivenin
GladstoneandBigg
(2001)forthedampingcoefficientdampofwavesin
sea‐iceasafunctionofsea‐icefractionicefrac:
3
0.5* 1 cos damp icefrac
[5]
The wave erosion velocity from White (1984) is
multipliedbythedampingcoefficient.Pleaseseethe
computercodepresentedintheappendix.
Eq (5) results in damping coefficients close to 1
below about 0.35 ice fraction, and damping
coefficientsclosetozeroforicefractionsgreaterthan
about0.85.
We tested our model against the results of EL‐
Tahanetal.(1987)Case2,foraverylarge
6
6.25 1 0
x
ton iceberg (1 ton is 1000 kg) melting in the Grand
Banks,withSST=3C,icefractionofzero,windspeed
of8m/sandaveragewaveheight=1.5m.Figure10
showstheaccuracyofourmodelisreasonable.
Figure10. Predicted iceberg length using melting model,
comparedtoobservedlength.
3 RESULTS
3.1 EnvironmentalVariables
Applying the methods listed in the previous section
yields the following correlations for environmental
parameters,foryears2016and2100,asafunctionof
month m from December to August, averaged in
LabradorandNewfoundlandwatersoutto5degrees
of longitude off‐shore. Month 0
is December, 1 is
January,etc.Theseequationsarenecessaryasinputs
to the melting model as it incrementally marches
forwardintimeinduringnumericalintegration:
SST2016(C)=‐0.002497m
6
+0.054923m
5
‐0.444948
m
4
+1.634709m
3
‐2.419993m
2
+0.348767m+
1.148874 [6]
SST2100(C)=‐0.003336m
6
+0.074290m
5
‐0.615148
m
4
+2.360881m
3
‐3.887948m
2
+1.000498m+
3.279805 [7]
WindSpeed2016(m/s)=0.036246m
3
‐0.412504m
2
+
0.451308m+10.533232 [8]
WindSpeed2100(m/s)=0.002019m
5
‐0.043250m
4
+
0.356252m
3
‐1.356886m
2
+1.430346m+9.687086[9]
IceCover2016(%ice)=‐0.01m
5
+0.2859m
4
‐2.183m
3
+1.2246m
2
+23.134m+12.601 [10]
IceCover2100(%ice)=‐0.0169m
6
+0.367m
5
‐2.5824
m
4
+5.2418m
3
+5.0516m
2
‐5.0192m+11.056 [11]
Transittime2016(days,wheremisthestarting
monthat60N)=1.6536m
2
‐3.2164m+57.95 [12]
465
Transittime2100(days,seenoteabove)=1.5714m
2
‐
3.9429m+70.286 [13]
The equations below for H* and F* apply to all
months, for fetches up to about 5 degrees longitude
off‐shoreinwatersoffLabradorandNewfoundland:
DimensionlesswaveheightH*=‐0.045376F*
3
+
13.820094F*
2
‐344.731632F* [14]
fetch cos 1
*
wave height
ice fraction
H
[15]
Dimensionlessfetch
1
2
*9.8 ) 1 /
F
fetch cos ice fraction wind speed
[16]
3.2 Effectofenvironmentalvariablesonmelting
If an extremely large iceberg drifts from northern
Labrador (60N) to the shipping lanes in
Newfoundland (48N latitude), the iceberg will
survivethejourneywithonlypartialmelting.When
the initial iceberg size is decreased in small
increments, the final size of
the iceberg at 48N
decreasesaswell,butatsomeinitialsizetheiceberg
melts just aftercrossing 48N.We refer to this initial
size as the Minimum Transit Size (MTS) – icebergs
smaller than the MTS succumb to melting on their
transit.WeuseMTStoquantifyincreasedmeltingas
wellastopredictfutureicebergnumbers.
Figure 11 was generated by looping our melting
modelthroughdecreasingicebergsizesuntilmelting
wasachieved.Thefigureshowstheminimumtransit
size(MTS)fromLabradortoNewfoundlandinyears
2100and2016,fortransitalongatypicalicebergpath
2.5 degrees
of longitude away from the shore. The
figure shows a significant increase in maximum
meltingsize,rangingfrom48%inDecemberto20%in
March.
Figure11.Icebergsmallestsizethatwillnotmeltintransit
from60Nto48Nforyears2100and2016
The effect of the greater melting on iceberg
numbersreaching48NcanbeestimatedfromNalcor
(2015), which recommends the equation below for
iceberglengthprobabilityofexceedanceinwatersoff
LabradorandNewfoundland:
0.017
128.23
L
Percentexceedance e
[17]
whereListhelengthoftheiceberginmeters.
Thedata used for Eq(17) were collectedin 1983,
and represent the best available information on
icebergsizes.
Inordertoestimatewhattheeffectthisincreased
meltingmighthaveonicebergnumbersdriftinginto
theshippinglanes,weassumethatsizedistributionin
2100and2016will be similartothat encountered in
1983(weareforcedtomakethisassumption,dueto
unavailabilityofotherreliable data). Wereasonthat
the percentage of icebergs of a given size surviving
thejourneyfrom60Nto48Nlatitude is
thesameas
the probability of exceedance. Figure 12 shows the
percentagesoftotalicebergsat60Nthatsurvivetheir
journeyto48N,asafunctionofthemonthat60N,for
years 2016 and 2100. Year 2100 bergs willreach the
shipping lanes 70 – 90 days later, assuming
no
groundings.
Figure 12. Percentage of icebergs in waters off
Newfoundland that will not succumb to melting on
theirjourneyfrom60Nto48N.
Figure 13 shows reductions in iceberg numbers
ranging from 40%‐50% for arrival dates between
March and July, which is when the bulk of the
icebergsexist below
48N.In August, when fewer or
no icebergs exist below 48N latitude, our analysis
indicates that iceberg numbers should be about the
samein2100as2016.
Figure13.Reductionsinicebergnumberscrossingintothe
shippinglanes,relativetoyear2016.
466
Figure14showsthecontributiontofuturemelting
ofbergsfollowinganaveragepath,duetoincreased
transittime,seasurfacetemperaturesandreductions
in sea‐ice concentration. Sea surface temperature
increasesareseentobethemostimportant,followed
byincreasedtransit timeanddecreased sea ice.It is
noted that a predicteddecrease in wind speed does
not by itself affect melting, although it is probably
responsible for at least a portion of the decreased
currentspeeds.Thewindhasasmalldirecteffecton
meltingfortworeasons:thewindspeedchangesare
relativelysmall,andwind
speeddirectlyaffectsonly
forcedconvectionbetweenseawaterandtheiceberg
– a component of the total heat transfer that is
eclipsedbyerosionduetowaveactionandcalving.
Figure14.
4 CONCLUSIONS
Increasesinseasurfacetemperature(SST),aswellas
decreasesinsea‐icecover,windandcurrentvelocities
will have a marked effect on iceberg melting off
NewfoundlandandLabrador.
The minimum length for icebergs surviving their
journey without succumbing to melting (MTS)
increases significantly in year 2100, as
compared to
current MTS values. For example, icebergs at N
Labrador in December of 2016 that are smaller than
156mwillmeltbeforereaching48N,butinyear2100
thelengthincreasesto228m.
Assuming future iceberg size distributions and
iceberg numbers off Labrador that are the same
as
today,icebergsdriftingintotheNWAtlanticshipping
lanesoffNewfoundlandarepredictedtosignificantly
decrease in numbers by year 2100.In March
throughJulycrossingsintotheshippinglanes(when
mostoftheicebergscrossintothearea)icebergswill
experience roughly 50% reductions in numbers, as
compared to
the present. These findings are
consistent with the range predicted by Han et al.
(2015) using extrapolations of environmental
parameters.
Theincreasedmeltingratesaredueto,inorderof
importance, increased sea‐surface temperatures
(responsiblefor66%oftheincreaseintheminimum
transitsize),decreasingcurrentvelocities(31%),
and
decreasing sea ‐ice cover (3%). Decreasing sea‐ice
tends to increase wave heights as well as accelerate
the effects of wave erosion; however, for the areas
studied the wave height is predicted to decrease
moderatelyinyear2100,byamaximumofabout10%
inDecember.
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APPENDIX
VBACodeforpredictingicebergmelting
'usesformulasfromWhiteandcalvingmodelfromSavage
'inputs
Dimxl(300)
sst=10.5'seasurfacetempdegreesC
rhoice=900'densitykg/m^3
kwater=0.569'thermalcondw/m‐k
visc=0.0018'viscositywaterkg/m‐s
ws=10#'windspeedm/s
wht=0.7'wavehtin
meters
rhowater=1000'waterdensitykg/m^3
tstep=0.5'timestepindays
vr=ws*0.017'icebergspeedreltowater,perel‐
tahan
deltaT=sst+1.8 'deltaTasSSTminusmelting
pointsuppressedbysalt
hfg=334'latentheatoffusionice
inJ/gram
tau=7'waveperiodinseconds
le=120'mlengthberg
xl(0)=le'initializeiceberglengtharray
ruff=0.02'bergroughnessinmeters
erol=0'initializeerosionduetowavemaking
volume=le^3 'initialvolume
kvisc=0.0000018'kinematicviscofwater
m^2/s
pr=0.0109*sst^2‐0.4922*sst+13.289'curve
fitfromwhitedata..for‐1<=T<=12
Open"berg"ForOutputAs#1'openoutputfile
Fori=1To(20/tstep)'loop
'**convectivelosses**
Re=vr*xl(i‐1)
/kvisc'Reynoldsnumber
Nu=0.055*(Re)^0.8*(pr)^0.4'Nusseltnumber
h=Nu*kwater/xl(i‐1)'heat/mass
transfercoefficient
q=h*deltaT*asurf'heatflowinwattstoberg
mlossConv=q/hfg*3600
*24/1000*tstep 'mass
lossbyconvectioninkg/tstep
vlossconv=mlossConv/rhoice'm^3lostper
tsteptoconvection
lLossconv=Nu*deltaT*kwater/(xl(i‐1)*hfg*
1000*rhoice)*3600*24*tstep
'lengthlossconv(m)
'**waveerosionlosses**
'recessionvelatperimeterinm/day
velwave=0.000146*(ruff/wht)^0.2*wht*
deltaT/tau*3600*24
erolthis=velwave*tstep'waveerosionthis
timestep(meter)
'forcalving
erol=erolthis+erol
'waveerosionlength
accumulatedsincelastcalve
tslab=0.196*xl(i‐1)'thicknessofslab(m)
overthewaveerosion,atcalving
failL=0.33*(37.5*wht+tslab^2)^0.5'notch
lengthatwhicherodedareabreaksunderownwt
'totalvolumeloss
lcalv=0.3*erolthis
xl(i)=xl(i‐1)‐lLossconv‐erolthis‐lcalv
10Print#1,i*tstep,xl(i)
lcalv=0
Nexti
Close#1
