ChangesinUgandanClimateRainfallatthe
VillageandForestLevel
1PaddySsentongo,3AbrahamJ.B.Muwanguzi,4UriEden,5TimothySauer,
3GeorgeBwanga,6GeoffreyKateregga,7LawrenceAribo,7MosesOjara,
3WilberforceKisambaMugerwa,1,2StevenJ.Schiff
May16,2017
arXiv:1705.05970[physics.ao-ph]
1CenterforNeuralEngineering,DepartmentofEngineeringScienceandMechanics,
2DepartmentsofNeurosurgeryandPhysics,ThePennsylvaniaStateUniversity,
UniversityPark,PA
3UgandanNationalPlanningAuthority,Kampala,Uganda
4DepartmentofStatistics,BostonUniversity,Boston,USA
5DepartmentofMathematics,GeorgeMasonUniversity,Fairfax,VA,USA
6MapUganda,Kampala,Uganda
7UgandanNationalMeteorologicalAuthority,Kampala,Uganda
Correspondence:
StevenJ.Schiff
CenterforNeuralEngineering
ThePennsylvaniaStateUniversity
UniversityPark,PA16802USA
[email protected]
Page 1 of 19
Abstract
In 2013, the US National Oceanographic and Atmospheric Agency refined the
historical rainfall estimates over the African Continent and produced the African
RainfallClimateversion2.0(ARC2)estimator.ARC2offersanearlycompleterecord
of daily rainfall estimates since 1983 at 0.1 x 0.1 degree resolution. Despite shortterm anomalies in twice-yearly rainy season intensities in Uganda, we identify an
overall decrease in average rainfall of about 12% during the past 34 years.
Spatiotemporally,thesedecreasesaregreatestinagriculturalregionsofcentraland
western Uganda, but are also reflective of rainfall decreases in the gorilla habitat
within the Bwindi Forest in Southwest Uganda. The findings carry significant
implicationsforagriculture,foodsecurity,andwildlifehabitat.
Page 2 of 19
Africaisboththedriestandhottestofcontinents,anditsavailablewater
is essential for almost all human activities and to support non-human
biodiversity.1In2013,theUSNationalOceanographicandAtmosphericAgency
refined the historical satellite-based rainfall estimates over the African
Continent and produced the African Rainfall Climate version 2.0 (ARC2)
estimator2. This estimator combines daily geostationary rainfall estimation
throughinfraredcloudreflectivitywithgroundbasedrainfallmeasurementsat
a fine grid scale at 0.1o x 0.1o resolution (approximately 11x11 km at the
Equator).Therecordreachesbackto1983,andcontinueswithreal-timedaily
data production. We here report an analysis of the stationarity and climate
patternsofrainfallaffectingUgandaovertheperiod1983-2016.
Therearemanycriticalusesofsuchdataatthisfineascale.Fromahuman
planningperspective,majorconstructionprojectscanbemappedtothemeanand
variability of rainfall for a given location or extent, and engineered to account for
anticipated extreme events. Additionally, agricultural planning can be adapted to
patternsandpredictedchangesinrainfall.Moreover,sinceinacountrylikeUganda
about 70% of the population depends on agriculture, these data may be used to
understandpopulationgrowthanddensityingivenregionsandthereforefacilitate
planning for settlements and economic activities. From a non-human perspective,
habitatlimitationsforendangeredspeciesmayplacetheirsurvivalatgreaterrisk.
Manyhumaninfectiousdiseaseshavestrongrelationshipstorainfall:cholera3,
malaria4, leptospirosis5, melioidosis6, and the seasonal Neisseria meningitis within
Page 3 of 19
theAfricanmeningitisbelt7.Infantinfectionsleadingtopostinfectioushydrocephalus
havebeennotedtohaveasignificantrelationshiptorainfall8.
Geographically, Uganda stretches from 1.43oS to 4.27oN and from 29.5oE to
35.03oE.At0.1ox0.1oresolutionUgandaiscontainedwithinasquare61x61grid.In
Figure1Aweillustratethecountryasacompositeoftheboundariesofthe44,034
villages that comprise the landmass, and superimpose the 3,721 satellite grids
overlay.
Theentiredatasetforall3,721timeseries(plottedinsequentialcolors)is
illustratedinFigure1B.Thecumulativerainfallover34yearsismappedontothe
satellitegridinFigure1C.FusingthesewiththecountrymapinFigure1D,thereare
severalnotablefeatures.Inthenortheast,thesemi-aridregionofKaramojaisshown
withlowcumulativerainfall.TheheaviestrainfallisinthenorthwestovertheCongo
Riverbasinrainforest.Theotherregionwithhighrainfalliswherethenortheastedge
ofLakeVictoriameetstheUgandanlandmassinthelowercentralregionoftheplot.
The averaged power spectral density of all 3,721 time series with error bounds is
showninFigure1E,whichreflectsthedominant1and2cycleperyearfrequencies,
and the spectrogram in Figure 1F demonstrates the consistency of these two
fundamental frequencies throughout the 34 year record. The 2-cycle per year
rainfallsintheEastAfricanHighlandsareofunequalsize,augmentingthe1-cycleper
yearfrequencyamplitude.
Statistically, rainfall distributions are often non-Gaussian due to nonnegativity and pronounced skewness. For such data, the normal distribution will
inadequatelyaccountfortherainfallvariability.Thisrendersordinaryleastsquares,
Page 4 of 19
with the assumed normal distribution of errors, a problematic choice for model
fitting. Indeed, the rainfall distribution for all 46,211,099 daily measurements is
highlyskewed(Figure2A),anditiswellknownthatsuchrainfalldatamayfollowa
gammadistribution9.Byaveragingacrossthe3,721spatiallocationsforeachdayin
time,andfilteringbetweenfrequenciesof1/20to6cyclesperyearforvisualization,
thetwice-yearlyrainyseasoncyclesarenowreadilyvisualized(Figure2B),andthe
distributionbecomesmuchlessskewedforthe12,419daysofdata(Figure2C).These
data can all be appropriately fit using the generalized exponential family of
distributionsmodeledwithintheGeneralizedLinearModel(GLM)frameworkthat
embracessuchdistributionsrangingfromgammatonormal.10
In Figure 2D we demonstrate a GLM fit to the 34 years of data, spatially
averagedforeachdayacrossthespatialgridbutnotfilteredovertime.Weshowboth
alog-linkedlinearfitwithtime(log(µ)=A+BT,whereµistheexpectedrainfall),as
wellasafitofbothtimeandalinearcombinationoffrequencies(using4,2,1,0.5,
and 0.25 cycles per year). There is a significant downward slope of the GLM
dependency on time of the spatially averaged rainfall by 12% over the 34-year
interval (slope of -0.0038 corresponding to an exp(-.0038)=0.38% reduction in
rainfallperyear,p<1.6x10-5,slopestandarderrorSE=0.00088),andthequalityof
thefitoftimeandfrequenciesisalsohighlysignificant(Fvsconstantmodel146,p<
7x10-317).
Toexaminethespatialcontributionstothisdecreaseinrainfall,wefit3,721
GLMmodelstoeachspatiallocation’stimeseries(withoutaveragingorfiltering).The
originoftheaveragenegativeslope,B,forthelinearmodelfit,log(µ)=A+BTinFigure
Page 5 of 19
2D,isbaseduponadistributionofslopeswithameanof-0.0031(0.31%reduction
peryear),wheretheprobability(fraction)ofnegativeslopesis0.78(2,902/3,721).
Wenowplottheseindividualslopesintheirspatiallocationonthesatellitegridin
Figure2E.Thecolormapforthespatialdistributionoftheseslopesusestheintensity
ofbrownandgreentorepresentthemagnitudeofthedecreaseorincreaseinslope
respectively.ThereisbroadregionincentralandwesternUgandathatappearstobe
responsiblefortheoveralldecreaseinrainfallshowninFigure2D.
These3,721slopes(Figure2E)representamassivemultipletestingproblem.
Toexplorethisspatialdistributionfurther,weturntothecontroloffalsediscovery
rate (FDR) using the method of Benjamini and Hochberg.11 We plot the curve
representing the GLM goodness of fit as p-values (in blue) in Figure 2F against a
familyofFDRsrangingfrom0.02to0.2,alongwiththestandardFDRforasingletest
(0.05)andtheBonferronicorrectedfalsepositiverateof1.3x10-5.Thedistributions
correspondingtotheseFDRsareshowninFigure3A,andtheircorrespondingspatial
mapsinFigure3B.Asthefalsediscoveryratesvaryfrom0.1totheBonferronirate,
identificationofthe regionofcentralandwestern Ugandawithdecreasingrainfall
overthese34yearsremainsrobust.
We can independently test these decreases in rainfall by taking difference
mapsofcumulativerainfallfordifferentperiodsoftime.InFigure3C,weillustrate
thedifferenceofcumulativerainfallinthefirstvsmostrecent15,10and5yearsof
thedata,alongwiththesecond5vsnexttolast5yearsegmentsofdata.Thespatial
maps illustrating increases or decreases in rainfall illustrating a broad region of
Page 6 of 19
decreased rainfall within central Uganda remain reflective of the GLM regression
slopesinFigure3Aand3B.
Next,weexaminetheBwindiImpenetrableForestwithinUganda.ThisForest
reserveconstitutesoneofthelastremaininghabitatsoftheMountainGorilla,andis
consideredcrucialforspeciessurvival.Groundbasedrainfalldataisunderstandably
incomplete12.Thecoordinatesofthe331squarekmBwindiForestlieswithin0.85oS
and -1.15oS, and 29.55oE and 29.85oE on the satellite map. These coordinates
correspondto16squaresofourgrid(Figure4A).ThecumulativerainfallfromARC2
isshowninFigure4B.Weagainfindthatthereisasignificantdownwardslopeofthe
GLMdependencyontimeofthespatiallyaveragedrainfallby12.8%overallyears
(slopeof-0.004correspondingtoa0.4%decreaseinrainfallperyear,p<0.01,slope
SE=0.00016),consistentwithourfindingsintheentiregrid.
Lastly, both the El Niño Southern Oscillation (ENSO) and the Indian Ocean
Dipole13 (IOD) are known to influence rainfall in East Africa.14 We turn to the
techniqueofwaveletcoherency,andseekastatisticalbootstrapthatpreservesmore
ofthepropertiesofthedatathanthewhite15orcolored16noiseemployedinprevious
workongeophysicalsystems.Followingtherecommendationforanon-parametric
bootstrapconstructedfromsurrogatedatafromtheoriginaltimeseries17,weuseda
randomization scheme previously employed by swapping binary partitions at
randomlocationsinatimeseries,18toensurethatlocalcorrelationsareeffectively
destroyed across an ensemble of such resampled time series, yet the relevant
frequenciesanddistributionofvaluesremainthesame.Applyingthisbootstrapped
statisticalmethod,thereareregionsatthe99%confidencelimitinthelatterhalfof
Page 7 of 19
our time series where ENSO (Figure 5A, 2006-2014, 1-2 year periods) and IOD
(Figure5B,2004-2015,1-4yearperiods)coherencywithrainfallremainssignificant.
TherelativelyshortlengthoftheinstrumentedARC2limitsouranalysisto34
years. Proxy and model simulation suggests that the IOD is more important than
ENSO over multidecadal and perhaps longer time scales.19 Although ENSO effects
interannualdroughts14,itislessimportantforinterdecadalrainfallpatterns20,and
our results are consistent with this. Nevertheless, our findings that ENSO and IOD
effectsonUgandanrainfallhavebeenmoresignificantwithinthemorerecenthalfof
the34-yearrecordremainsunexplained.
The weather patterns in East Africa are unusually complex and regionally
disparate21. Uganda is at the western edge of the Greater Horn of Africa22 (GHA)
region,andhashistoricallyhadmorerainfallthanneighboringKenyaandTanzania21.
AlthoughmanyclimatemodelspredictthatEastAfricawillexperienceanincreasein
rainfall as the planet’s atmosphere warms, it has in fact become drier over recent
decades19,andresolvingthisdiscrepancyhasbeenatopicofactiveresearch.20
One of the hazards in generalizing from regional models to more localized
regions,orextrapolatingusingproxydatatakenfromhighlylocalizedsedimentcore
analysis23, is that predictions may not equally apply to all countries within such
regions.Forinstance,themulti-decadalinfluenceonEastAfricanrainfallpredicted
fromIODdynamics19isnotwellreflectedinour34-yearUgandandataset,wherethe
effectsappearsub-decadal.
How such rainfall decreases impact infectious disease prevalence and risks
will be determined by individual disease characteristics, and will be important for
Page 8 of 19
specificlocations.Byfusingthesatelliterainfallgridwiththelocationsofallofthe
villages in Uganda, we have a finely granular way to track epidemic disease. Such
fusionisaplatformforseekingoptimizationoftreatment,andprevention,ofmany
infectiousdiseases.
Although climate is global and regional, policy and preparation remains
largely dependent upon individual countries. Uganda is a country where 72% of
geographicalareaisusedforrain-fedfarmingandthepopulationgrowthisoneofthe
highest in the world.12 An average rainfall decrease of this magnitude, over the
multipledecadesoftheclimaterecordexaminedhere,isimportantforagriculturein
acountrydependentonsubsistencecropyields.Thereisasubstantialneedformore
granularandaccuratepredictionmodelingforbothshort-termdroughtanticipation
and longer-term rainfall trends within the time-frame relevant for economic
planning.Nevertheless,thepresenttrendinrainfalldecreaseisgradualenoughso
thatthereremainsanopportunitytobuildadaptivecapacity1throughstrategies22to
makethecountrymoreresilient:anticipatoryland-usemanagement,shiftstowards
moresustainableagriculturalpractices,andinfrastructuredevelopmenttoincrease
theresiliencyofthesocietywithrespecttoshortandlong-termchangesinrainfall.
Acknowledgements:
WearegratefultoFredrickKayanja(GuluUniversity),MujuniGodfrey(UNMA),
TumusiimeMoses,(UNMA),GodwinAyesiga(UNMA),OtimF.C.Obeke(UNMA),
TenywaJoseph(NPA),SajjabiFredrick(NPA),OngoraEmmanuel(NPA),Namyalo
Jackie(NPA),ArineitweJustine(NPA),andTebugulwaAllen(NPA),fortheirhelpful
discussions.SupportedbyUSNIHPioneerAward5DP1HD086071.
Page 9 of 19
Methods
Data
Rainfalldatawasobtainedfromthegridded,daily34yearprecipitationestimation
dataset(http://www.cpc.noaa.gov/products/international/data.shtml)centeredoverAfrica
at0.1ox0.1ospatialresolution,theAfricanRainfallClimatology,version2(ARC2)2.
Thesedataareanestimationderivedfromafusionofthegeostationaryinfrared
sensingfromtheEuropeanOrganisationfortheExploitationofMeteorological
Satellites,and24hourrainfallmeasurementsfromGlobalTelecommunication
Systemgaugeobservations.Thereare341missingdaysintheseARC2data(outof
12,419days)whichwereaccountedforbylinearinterpolation.
ElNinoSouthernOscillationdata(ENSO)wasobtainedfromNOAAat
https://www.esrl.noaa.gov/psd/enso/mei/table.html.Thesemonthlydatathrough
2016wereexpandedbasedonthelengthofeachmonthintoequivalentdailydata.
IndianOceanDipole(IOD)datawasobtainedfromTheExtendedReconstructedSea
SurfaceTemperature(ERSST)datasetderivedfromtheInternational
ComprehensiveOcean–AtmosphereDataset(ICOADS)atNOAAat
https://iridl.ldeo.columbia.edu/SOURCES/.NOAA/.NCDC/.ERSST/.version4/.IOD/.C
1961-2015/.iod/datatables.html.Thesemonthlydatathrough2015wereexpanded
basedonthelengthofeachmonthintoequivalentdailydata.
ThegeocodedmapofUgandaatthevillagelevelwascompiledemployingcensus
andelectioncommissionrecords,andpublicallyaccessibleat[urltobeestablished
attheUgandanNationalPlanningAuthoritywithpublicationofthispaper].
SignalProcessing
Spectrawerecalculated,followingremovalofthemeanfromeachofthe3,721time
series,usingHammingdatawindows3-yearsinlength(3*365days),with95%
overlapofthesewindows,and1-sidedspectralestimationsperformedusing
Welch’smethodasimplementedinMatlabfunctionpwelch.24Thepowerspectral
density(PSD)fromeachofthe3,721timeseriesfromthedifferentlocationswere
Page 10 of 19
thenaveraged,andplottedonadecibelscale(10*log(PSD))inFigure1Efor
frequenciesgreaterthanzeroandlessthan12cyclesperyear.Thespectrafrom
eachwindowedtimeperiodwerethenassembledintothespectrograminFigure1F.
Whenfilteringwasapplied,suchasinFigure2B,weemployedabandwidthof1/20
to6cyclesperyear,anorderof100,frequencyof365daysperyear,Nyquist
frequencyof365/2,andafiniteimpulseresponse(FIR)filter(Matlabfunctionfir1)
appliedinazero-phasedistortionmannerusingMatlabfunctionfiltfilt.Thespatial
meanofall3,721filteredtimeserieswereplottedinFigure2C.
Whenemployedinwaveletcoherency,boththespatiallyaveragedrainfalltime
series(through2015),andENSOtimeserieswereequivalentlyfilteredwithinthe
same1/20–6cycleperyearbandwidth.
StatisticalAnalysis
GeneralizedLinearModeling
Weimplementedgeneralizedlinearmodeling(GLM)usingthemethodsdeveloped
byNelderandWedderburn.10,25UsingtheimplementationoftheMatlabfunction
glmfit,weemployedgammadistributionsandloglinkfunctions.
Thefalsediscoveryrate(FDR)wascontrolledusingthemethodofBenjaminiand
Hochberg.11AfamilyofFDRrateswasdeveloped,assumingthatthefalsepositive
(TypeI)errorratewasa(nominally0.05),thenumberofcomparisonstestedwas
m,asthelargestp(i),where:
𝑝 𝑖 ≤𝛼∗
𝑖
,
𝑚
0 ≤ 𝑖 ≤ 𝑚.
Thesep(i)thresholds,forafamilyofFDRrates,areshownasintersectionsbetween
theblueandredlinesinFigure2F.
Waveletcoherence
WeemployedthemethodofTorrenceandWebster15,asimplementedintheMatlab
functionwcoherence,exceptwereplacetheirwhitenoisesurrogatewithsurrogates
Page 11 of 19
baseduponrandomlypartitioned18andtimereversedsurrogatesbasedupononeof
thetimeseries.Wechosethepartitionedsectionsoftherandomly,swappingthe
partitionorder.Thishasprovenarobustmethodtobreakupshortterm
correlationsbetweentwotimeseries,whilepreservingthestatisticalproperties
otherthanlosingtheslowestoffrequenciesduetothepartitioning.Unlike
preservingspectrabyrandomizingthephasesoffrequenciesinaFouriertransform,
andtheninvertingthetransform,thismethodalsopreservestheoriginaldata
valuesanddistribution,18andismuchmorecomputationallyefficientthan
simulatedannealingalternatives.26Wecreatedanensembleof1000suchsurrogate
waveletcoherencies,chosethelargest95%or99%surrogatecoherenciesateach
pointinthetime-frequencyplot,andusedthesethresholdstobuildour
bootstrappedconfidencelimitssettingallvaluestozerowhichdidnotexceedthese
thresholds.Weplottheremainingsignificantwaveletmagnitude-squared
coherenciesinthesignificanceplotsofFigure5.
Codeavailability
Thedatasets,andMatlabcoderequiredtoreplicatethefindingsofthispapers,are
openlyavailableat[urlwithdurablelinktobeestablishedatthetimeofpublication
ofthispaper].
Page 12 of 19
Figure1
Figure1.FusionofsatelliterainfalldatawithmapofUgandaatthevillagelevel.Shownarethepattern
ofcumulativerainfalloverthe34yeardataset,andthefrequencycontentoftherainfall
demonstratingtwice-yearlyrainyseasons.A)SatellitegridoverlayoverUgandashowingthe44,034
villagesaspolygons,overlainwiththe61x61,0.1ox0.1o,satellitegrid.B)Rainfallperdayfromeachof
3721gridlocationsfor12,340days.C)Cumulativerainfallon61x61gridforall12,419daysover34
yearsfrom1983–2016.D)Fusionofcumulativerainfallwithvillageandcountrymap.Notethatthe
heaviestrainsareovertherainforestwithintheCongoRiverBasintothewestofUganda,andwhere
thenortheastcornerofLakeVictoriaabutstheUgandanlandmass.Thedriestregionisinin
northeastUganda,wheretheKaramojadistrictabutsnorthwestKenyaandSouthSudan.E)Spectral
densityestimatedfromeachof3,721gridlocationsover12,419days,withmeanand±1SD.Hanning
windowof3x365with95%overlap.Pointsplottedasdecibels(10log10).F)Spectrogramwithmean
removedfromsignal.Notethedominantrainycyclesat1and2xperyear.
Page 13 of 19
Figure2
Figure2.Spatiallyaveragedrainfalldemonstratesadecreaseoverthe34yearrecord.Thenatureofthe
datawithandwithoutspatialaveragingisshown,andtheoriginoftheaveragedecreaseinrainfall
explainedbythegeographicaldistributionofdecreasesandincreasesinrainfall.A)Histogramofdaily
rainfallforalldaysandlocations,truncatedbelow40mmrainperday.B)Dailyrainfallspatiallyaveraged,
andfilteredwithfiniteimpulseresponsefilter(order100)forfrequencies0.05-6cyclesperyear.Filter
appliedwithzerophasefilteringforwardsandbackwards.Thetwice-yearlyrainyseasonsintheEast
AfricanHighlandsarenowplainlyseen.Twodroughtanomaliesfromdroughtsinfallrainyseasonfailures
areindicatedfor2010and2016withblackarrows.TheaveragedandfiltereddatasetfromB
demonstratesamuchlessskeweddistributioninC.D)LinearGLMfit,log(µ)=A+BT,shownbyyellowline,
andfullmodelfittedwith0.25,0.5,1,2,and4cycleperyearfrequenciesshownbyredline,superimposed
onspatiallyaveragedbutunfiltereddatainD.InEareshowntheindividualslopesoflinearGLM
regressiontoeachgridpointtimeseries,withnoaveraging,onascaleillustratingtheintensityofthe
negative(brown)orpositive(green)slopes.F)FalseDiscoveryRate(FDR)plotfortheGLMfitp-values
fromtheslopeplotinE,forafamilyofFDRvalues.Theintersectionsofthesortedp-values(blue)withthe
Benjamini-Hochbergcoefficients(redlines)formtheFDRthresholdsemployedinFigure3.
Page 14 of 19
Figure3
Figure3.Thedecreaseinrainfallisarobustfinding.Wefirstperformedanexploration
offalsediscoveryrates,andthenindependentlytestedwithcumulativerainfall
differences.A)Histogramofthe3,721GLMslopesfrominFigure2E.Withprogressively
moreconservativeFDRrates,weseetheprogressiveeliminationofsmallmagnitude
slopes,culminatinginthemostconservativethresholdingwithBonferroni(a/3721).In
Bwemapthesedistributionsofslopesbackontothesatellitegrid.Notethatthemost
significantslopesretainthecoherentregionsofcentralandwesternUgandawherethe
rainfalldecreasesthemostoverthehistoricalrecord.Toindependentlytestthese
findings,weexaminethedifferencemapsofcumulativerainfallfromtherawARC2data
inC.Indeed,forthefirstandmostrecent15,10,and5yearcumulativedata,andthe
secondandsecond-to-last5yearperiods,thedifferencemapsretainthesamerainfall
patternofdecreaseindicatedfromtheGLMfits.
Page 15 of 19
Figure4
Figure4.ThedecreaseinrainfallisalsoreflectedwithintheBwindiImpenetrableForest
region.ThisisoneofthelastremaininghabitatsoftheMountainGorilla.A)TheBwindi
ImpenetrableForestinUganda(yellow),coveredby16ofthesatellitegrids.Figure11.
B)Cumulativerainfallfrom1983-2016withinterpolatedshadingovertheBwindi
coordinates.C)SpatiallyaveragedfilteredtimeseriesoftheBwindirainfall,overlain
withtheGLMmodelsasinFigure2.Notethesubstantialrainfalldecreaseoverthe
record.
Page 16 of 19
Figure5
Figure5.ElNinoSouthernOscillation(ENSO)andIndianOceanDipole(IOD)
relationshiptospatiallyaveragedrainfall.Withrigorousstatisticalconfidencebounds,
thereisacoherencybetweentheseindicesandtheUgandanrainfall,butonlyinrecent
years,andonlyforrelativelyshortperiodsfrom1-4years.A)Waveletcoherency
betweenspatiallyaveragedandfilteredrainfall,withtheENSOindexinterpolatedfrom
monthlytodailyvalues,andfilteredidenticallyasrainfalldata.Thesecondpanel
reflectsthemeanof1000surrogatecoherencycalculations,fromwhich95%(third
panel)and99%(fourthpanel)confidencelimitsrevealonlytheregionsthatmetthese
significancecriteria.Theconeofinfluence,delimitingwhereedgeeffectssubstantially
confoundtheanalysis,isindicatedbythewhitedottedline.B)identicalcalculationsfor
theIODindex.ThemostsignificantcoherenciesbetweenENSOandIODoccursduring
themostrecent10years,withperiodsfrom1-4years.
Page 17 of 19
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