Simulang and forecasng seasonal ice cover 1147 · Simulang and forecasng seasonal ice cover...
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Simula’ng and forecas’ng seasonal ice cover Xiaolong Ji 1 , Houraa Daher 1 , Rebecca Bolinger 2 , Andrew Gronewold 2 , Richard B. Rood 1 1 College of Engineering, Climate and Space Sciences and Engineering, University of Michigan 2 NOAA Great Lakes Environmental Research Laboratory Summary Future Work Result References • Past research has shown that teleconnec@on paBerns (Fig. 3) are related to the ice cover in Great Lakes region. • For the Apostle Islands (Fig. 2), we use two separate sta@s@cal models (e.g., beta model and Poisson model) to predict whether solid ice will happen, and when is the first date of solid ice in a given year. • The results show that we can predict whether solid ice will happen quite well and a 10% confidence interval for the first date of solid ice indicates a safe @me for the Na@onal Park Service to prepare to open the ice caves (Fig. 1) for visitors. Grand Portage National Monument Thunder Bay Boundary Waters Canoe Area Voyageurs National Park Pictured Rocks National Lakeshore N Madeline Basswood Hermit Oak Stockton Gull Michigan Manitou Otter Rocky South Twin North Twin Ironwood Cat Outer Ù C a nada United States L a k e S u p e r i o r O n tario M in n e s o ta Michigan Wisconsin Minnesota Wisconsin 61 Duluth Superior 13 Bayfield Wisconsin Park Boundary Eagle Sand York Raspberry Bear Devils Long Copper Harbor Keweenaw Peninsula Marquette Ù 41 Ù 8 Cameron Eau Claire Heafford Junction St. Croix Falls Minneapolis st. Paul Û 35 Location Isle Royale National Park S t . C ro i x N a t i o n al S c e n ic R i v e r wa y 0 25 50 Miles Indian Reservation N No Scale 633•20075•DSC•6/2003 Ice year maximum of 10−day average ice cover % 1973 1978 1983 1988 1993 1998 2003 2008 2013 0 20 40 60 80 100 probability of the max of 10−day average ice cover GE 90 % whether solid ice happened historically 0 1 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 • Update ice area data (2016 & 2017). • Rolling forecast verifica@on. Sergei Rodionov, Raymond A. Assel, Winter severity in the Great Lakes region: a tale of two oscilla@ons[J], CLIMATE RESEARCH, Vol. 24: 19 –31, 2003. Katherine Van Cleave, John D. Lenters, Jia Wang, and Edward M. Verhamme, A regime shie in Lake Superior ice cover, evapora@on, and water temperature following the warm El Nino winter of 1997–1998[J], Limnology and oceanography, Vol. 59, Issue 6: 1889-1898, November 2014. Aug Sep Oct Nov Dec Avg ao X X X X X nino X nao X X X X pdo X pna X X X X X soi 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 Table 2. Selected variables based on step-wise regression analysis. Figure 1. Every year, many people spend their vaca@ons exploring the beau@ful sceneries of the Apostle Islands ice caves, which form in winter. Predic@ng the first date on which the ice is solid enough to walk upon is important to the Na@onal Park Service. Credit: Photo of the Apostle Islands Ice Caves by Instagram user @semilgee. Figure 2. Map of the Apostle Islands. Credit: Na@onal Park Service. Can be accessed at hBps://www.nps.gov/apis/planyourvisit/ maps.htm Data & Methods Figure 4. Daily ice cover from 1973 to 2015 using data from the Na@onal Ice Center (NIC), interpolated by NOAA Great Lakes Environmental Research Laboratory (GLERL). 0 40 80 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 0 40 80 1987 1988 1989 1990 1991 1992 1993 1994 Ice cover % 1995 1996 1997 1998 1999 2000 0 40 80 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 0 40 80 Jan Apr 2015 ice cover 10day avg 90% The first date of solid ice Dec Jan Feb Mar Apr 1973 1978 1983 1988 1993 1998 2003 2008 2013 Figure 5. The first day on which the 10-day average ice cover surrounding the Apostle Islands exceeded 90%. Seasons without a data point indicate a year when 10-day average ice cover did not exceed 90%. Figure 3. We used the data from 6 teleconnec@ons: AO, NINO3.4, NAO, PDO, PNA, SOI. Credit: UCAR. Can be accessed at: hBps://www2.ucar.edu/ atmosnews/perspec@ve/6717/twisters- and-teleconnec@ons Before building the model, we first check the correla@on within and between teleconnec@ons to prevent the mul@-colinearity problem. The results shows that NINO 3.4, PDO and SOI all have significant temporal autocorrela@on (Fig. 6). Table 1 Figure 6. The temporal correla@on of NINO 3.4 from August to December. We also find that PDO is correlated to SOI for every month, and that AO and NAO are highly correlated in the month of December (figure not shown). Here, highly correlated means over 70%. Thus, we finally have 16 different teleconnec@on variables, which can be seen in Table 1. As can be seen in Fig. 4, there are a few years that the 10-day average ice cover didn’t reach 90%, which means there’s no safe solid ice in that year. To solve this problem, we built a separate model to predict maximum of 10-day average ice cover indirect way (Fig. 7a, b). In Fig. 7b, if the probability is small and no ice is observed, that means that our model does a good job of predic@ng no solid ice. Similarly, if the probability is large and ice is observed, the predic@on of solid ice is also good. On the other hand, if the probability is small but ice is observed, (Type I error) which means we predict no solid ice but it occurs, Na@onal Park Service will lose money for these days. If the probability is large but no ice is observed, (Type II error) which means we predict solid ice but it doesn’t occur, someone might lose their lives. No@ce that when probability is greater than 35%, only 1 year in history has Type II error, while if the probability less than 35%, 2 years have Type I error. Thus, we draw the constant probability line at 35% (red line) on the plot as the index of the uncertainty of the predic@on. (Can be moved according to Na@onal Park Service). If the predic@on probability is on the lee side of the red line, then the solid ice has a low chance to occur. If the predic@on probability is on the right side, solid ice has a high chance to occur. Figure 8. 90% observed (black dots) and simulated (ver@cal lines) represents 95% predic@on intervals for the first onset of safe ice cover. Blue horizontal segments represent the 0.1 probability exceedance threshold (i.e., there is roughly a 0.1 probability that ice cover will be safe before that date). Figure 7a. Time series of observed (black) and simulated (red) maximum 10-day average ice cover. Gray regions report 95% predic@on intervals of our model. Blue link added for reference (90%). Figure 7b. Rela@onship between observed occurrence of “safe” ice cover (y axis; 0=unsafe and 1= safe) and model simulated probability of safe ice cover. Red line indicates proposed decision threshold for NPS manager. We then use the fiBed model to predict the 10-day average ice cover and check whether or not it is greater than 90%. If the 10-day average ice cover is greater than 90%, then there’ll be solid ice in that year. Furthermore, we use the corresponding and to calculate the two shape parameters and fit into the beta quan@le func@on in R to get the probability. The comparison between the probability and whether or not solid ice occurred can help us decide a standard of the uncertainty of our predic@on. μ ϕ y i ∼ β μ i , ϕ ( ) f ( y; μ , ϕ ) = Γ ( ϕ ) Γ ( μϕ ) Γ ((1 − μ ) ϕ ) y μϕ − 1 (1 − y ) (1 −μ )ϕ − 1 ,0 < y < 1 y i , where is the maximum of 10-day average ice cover we are going to predict in i-th year; and are the mean and precision parameters follow beta distribu@on ϕ μ i the corresponding shape parameter can be accessed by μ = p / p + q ( ) and ϕ = p + q λ is the mean and variance of y. Stepwise func@on is also used in Poisson model to do the model iden@fica@on. Here y is the number of days from Dec. 1 st and x is the teleconnec@on data. The second model, predic@ng the expected the first onset date of solid ice, is a Poisson model (Fig. 8). p ( y|x ;θ ) = λ y y ! e − λ log ( E ( Y | x) ) =α + β ʹ x , where α ∈ R β ∈ R n and , , Total 8 6 Independent Variable selected for regression analysis aeer checking for correla@on (Figure 6). 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.nino3.4 sep.nino3.4 oct.nino3.4 nov.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 Beta Model 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 13 Independent • Impact of date of forecast. • Impact of Hazard model (instead of Poisson). 1147 Solid ice is predicted but not observed. Solid ice is predicted and observed Solid ice is observed but not predicted. Solid ice is not observed and not predicted. 2000 1999 1989 1998
Transcript of Simulang and forecasng seasonal ice cover 1147 · Simulang and forecasng seasonal ice cover...
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
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
