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Simula'ngandforecas'ngseasonalicecoverXiaolongJi1,HouraaDaher1,RebeccaBolinger2,AndrewGronewold2,RichardB.Rood1

1CollegeofEngineering,ClimateandSpaceSciencesandEngineering,UniversityofMichigan2NOAAGreatLakesEnvironmentalResearchLaboratory

Summary

Future Work

Result

References

•  Pas t r e sea r ch ha s shown tha tteleconnec@on paBerns (Fig. 3) arerelated to the ice cover in Great Lakesregion.

•  For the Apostle Islands (Fig. 2), we usetwo separate sta@s@cal models (e.g.,beta model and Poisson model) topredict whether solid ice will happen,andwhenisthefirstdateofsolidiceinagivenyear.

•  The results show that we can predictwhether solid icewill happen quitewelland a 10% confidence interval for thefirstdateofsolidiceindicatesasafe@mefor theNa@onal Park Service to preparetoopentheicecaves(Fig.1)forvisitors.

Grand PortageNationalMonument

ThunderBay

Boundary WatersCanoe Area

VoyageursNational Park

Pictured RocksNational Lakeshore

!N

MadelineBasswood

Hermit

Oak

Stockton

Gull

Michigan

ManitouOtter

RockySouthTwin

NorthTwin

Ironwood

Cat

Outer

Ù

CanadaUnited States

Lake Super ior

OntarioMinnesota

MichiganWisconsinMin

neso

taW

isco

nsin

61

Duluth

Superior

13

BayfieldWisconsin

Park Boundary

Eagle

Sand YorkRaspberry

Bear

Devils

Long

Copper Harbor

Kew

eena

wPe

ninsula

MarquetteÙ41

Ù8Cameron

Eau Claire

Heafford Junction

St. CroixFalls

Minneapolis

st.Paul

Apostle Islands National Lakeshore

Û35

Location

IsleRoyale National Park

St.Croix National Scenic

Riv

erway

0 25 50 Miles

IndianReservation

!N

No Scale

633•20075•DSC•6/2003

U.S. Department of the InteriorNational Park Service

Ice year

max

imum

of 1

0−da

y av

erag

e ic

e co

ver %

1973 1978 1983 1988 1993 1998 2003 2008 2013

020

4060

8010

0

probability of the max of 10−day average ice cover GE 90 %

whe

ther

sol

id ic

e ha

ppen

ed h

isto

rical

ly

01

0 10 20 30 40 50 60 70 80 90 100

Dec

Jan

Feb

Mar

Apr

1973 1978 1983 1988 1993 1998 2003 2008 2013

•  Updateiceareadata(2016&2017).•  Rollingforecastverifica@on.

SergeiRodionov,RaymondA.Assel,WinterseverityintheGreatLakesregion:ataleoftwooscilla@ons[J],CLIMATERESEARCH,Vol.24:19–31,2003.

KatherineVanCleave,JohnD.Lenters,JiaWang,andEdwardM.Verhamme,AregimeshieinLakeSuperioricecover,evapora@on,andwatertemperaturefollowingthewarmEl Nino winter of 1997–1998[J], Limnology and oceanography, Vol. 59, Issue 6:1889-1898,November2014.

Aug Sep Oct Nov Dec Avgao X X X X Xnino Xnao X X X Xpdo Xpna X X X X Xsoi

Poisson Aug Sep Oct Nov Dec Avg

ao X X

ao^2 X

nao X X

nao^2 X X

pna

pna^2 X

pdo

pdo^2

nino

Nino^2

Table2.Selectedvariablesbasedonstep-wiseregressionanalysis.

Figure1.Everyyear,manypeoplespendtheirvaca@onsexploringthebeau@fulsceneriesoftheApostleIslandsicecaves,whichforminwinter.Predic@ngthefirstdateonwhichtheiceissolidenoughtowalkuponisimportanttotheNa@onalParkService.Credit:PhotooftheApostleIslandsIceCavesbyInstagramuser@semilgee.

Figure2.MapoftheApostleIslands.Credit:[email protected]://www.nps.gov/apis/planyourvisit/maps.htm

Data & Methods

Figure4.Dailyicecoverfrom1973to2015usingdatafromtheNa@onalIceCenter(NIC),interpolatedbyNOAAGreatLakesEnvironmentalResearchLaboratory(GLERL).

040

80

1973 1974 1975 1976 1977 1978 1979

1980 1981 1982 1983 1984 1985 1986

040

80

1987 1988 1989 1990 1991 1992 1993

1994

Ice

cove

r %

1995 1996 1997 1998 1999 2000

040

80

2001 2002 2003 2004 2005 2006 2007

2008 2009 2010 2011 2012 2013 2014

040

80

Jan Apr

2015

ice cover10day avg90%

The

first

dat

e of

sol

id ic

e

Dec

Jan

Feb

Mar

Apr

1973 1978 1983 1988 1993 1998 2003 2008 2013

Figure5.Thefirstdayonwhichthe10-dayaverageicecoversurroundingtheApostleIslandsexceeded90%.Seasonswithoutadatapointindicateayearwhen10-dayaverageicecoverdidnotexceed90%.

Figure3.Weusedthedatafrom6teleconnec@ons:AO,NINO3.4,NAO,PDO,PNA,SOI.Credit:UCAR.Canbeaccessedat:hBps://www2.ucar.edu/atmosnews/perspec@ve/6717/twisters-and-teleconnec@ons

Before building the model, we first check the correla@on within andbetween teleconnec@ons to prevent the mul@-colinearity problem. Theresults shows that NINO 3.4, PDO and SOI all have significant temporalautocorrela@on(Fig.6).

Table1

[email protected].

WealsofindthatPDOiscorrelatedtoSOIforeverymonth,andthatAOand NAO are highly correlated in the month of December (figure notshown).Here,highlycorrelatedmeansover70%.Thus,wefinallyhave16differentteleconnec@onvariables,whichcanbeseeninTable1.

AscanbeseeninFig.4,thereareafewyearsthatthe10-dayaverageicecoverdidn’treach90%,whichmeansthere’snosafesolidiceinthatyear.Tosolvethisproblem,webuiltaseparatemodeltopredictmaximumof10-dayaverageicecoverindirectway(Fig.7a,b).

InFig.7b,iftheprobabilityissmallandnoiceisobserved,[email protected],iftheprobabilityislargeandiceisobserved,[email protected],iftheprobabilityissmall but ice is observed, (Type I error) which means we predict no solid ice but itoccurs,Na@onalParkServicewill losemoneyfor thesedays. If theprobability is largebutno ice isobserved, (Type IIerror)whichmeanswepredict solid icebut itdoesn’toccur,someonemightlosetheirlives.No@cethatwhenprobabilityisgreaterthan35%,only1year inhistoryhasType IIerror,while if theprobability less than35%,2yearshaveTypeIerror.Thus,wedrawtheconstantprobabilitylineat35%(redline)ontheplot as the index of the uncertainty of the predic@on. (Can be moved according toNa@onal Park Service). If the predic@on probability is on the lee side of the red line,thenthesolidicehasalowchancetooccur.Ifthepredic@onprobabilityisontherightside,solidicehasahighchancetooccur.

Figure8.90%observed(blackdots)andsimulated(ver@callines)represents95%predic@onintervalsforthefirstonsetofsafeicecover.Bluehorizontalsegmentsrepresentthe0.1probabilityexceedancethreshold(i.e.,thereisroughlya0.1probabilitythaticecoverwillbesafebeforethatdate).

Figure7a.Timeseriesofobserved(black)andsimulated(red)maximum10-dayaverageicecover.Grayregionsreport95%[email protected](90%).

Figure7b.Rela@onshipbetweenobservedoccurrenceof“safe”icecover(yaxis;0=unsafeand1=safe)andmodelsimulatedprobabilityofsafeicecover.RedlineindicatesproposeddecisionthresholdforNPSmanager.

We thenuse thefiBedmodel topredict the10-day average ice cover andcheckwhetherornotitisgreaterthan90%.Ifthe10-dayaverageicecoverisgreaterthan90%,thenthere’llbesolidiceinthatyear.

Furthermore,weusethecorresponding andtocalculatethetwoshapeparametersandfitintothebetaquan@[email protected] comparison between the probability and whether or not solid iceoccurredcanhelpusdecideastandardoftheuncertaintyofourpredic@on.

µ ϕ

yi ∼ β µi,ϕ( )

f (y;µ,ϕ ) = Γ(ϕ )Γ(µϕ )Γ((1−µ)ϕ )

yµϕ−1(1− y)(1−µ )ϕ−1,0 < y <1

yi,whereisthemaximumof10-dayaverageicecoverwearegoingtopredictini-thyear;andarethemeanandprecisionparametersfollowbetadistribu@on

ϕµi

thecorrespondingshapeparametercanbeaccessedby µ = p / p+ q( ) and ϕ = p+ q

λisthemeanandvarianceofy.Stepwisefunc@onisalsousedinPoissonmodeltodothemodeliden@[email protected]@ondata.

Thesecondmodel,predic@ngtheexpectedthefirstonsetdateofsolidice,isaPoissonmodel(Fig.8).

p( y|x ;θ ) = λy

y! e−λ

log (E(Y | x) ) =α +βʹx ,where α ∈ R β ∈ Rn and,

,

Total 8 6Independent

Variableselectedforregressionanalysisaeercheckingforcorrela@on(Figure6).

Corr:0.97

Corr:0.944

Corr:0.973

Corr:0.914

Corr:0.94

Corr:0.984

Corr:0.894

Corr:0.918

Corr:0.964

Corr:0.987

aug.nino3.4 sep.nino3.4 oct.nino3.4 nov.nino3.4 dec.nino3.4

aug.nino3.4sep.nino3.4

oct.nino3.4nov.nino3.4

dec.nino3.4

−1 0 1 −1 0 1 2 −1 0 1 2 −2 −1 0 1 2 −2 −1 0 1 2

0.0

0.2

0.4

0.6

−1

0

1

2

−1

0

1

2

−2

−1

0

1

2

−2

−1

0

1

2

BetaModel

Aug Sep Oct Nov Dec Avg

ao X X X X

ao^2 X X

nao X X

nao^2 X X

pna X

pna^2 X X

pdo X

pdo^2 X

nino

Nino^2 X

Total 16 13Independent

•  Impactofdateofforecast.

•  ImpactofHazardmodel(insteadofPoisson).

1147

Solidiceispredictedbutnotobserved.

Solidiceispredictedandobserved

Solidiceisobservedbutnotpredicted.

Solidiceisnotobservedandnotpredicted.

2000

1999

1989

1998