533
1 INTRODUCTION
Safety at sea is depends greatly on the sea surface
conditions. Oceanographic models are utilized to
produceforecastsofseasurfaceinformation,enabling
thepredictionoftheseconditions.Europeanagencies,
such as FRONTEX, require access to met‐ocean
information for pan‐European seas, including the
Aggregating Sea Surface Hydrodynamic Forecasts From
Multi-Models for European Seas
V.Frishfelds,J.She,J.Murawski&J.W.Nielsen
DanishMeteorologicalInstitute,Copenhagen,Denmark
ABSTRACT: Maritime information services supporting European agencies such as the FRONTEX require
European‐wide forecast solutions. Following a consistent approach, regional and global forecasts of the sea
surfaceconditionsfromCopernicusMarine Serviceand national met‐oceanservicesareaggregatedinspace
andtimetoprovide
aEuropean‐wideforecastserviceonacommongridfortheassistanceofSearchandRescue
operations. The best regional oceanographic model solutions are selected in regional seas with seamless
transitiontotheglobalproductscoveringtheAtlanticOcean.TheregionalforecastmodelscovertheBlackSea,
MediterraneanSea,Baltic
Sea,NorthSeaand combine the North Sea– Baltic SeaattheDanishstraits. Two
global models have been added to cover the entire model domain, including the regional models. The
aggregatedproductisrequiredtohaveanupdatefrequencyof4timesadayandaforecastingrangeof
7days,
whichmostoftheregionalmodelsdonotprovide.Therefore,smoothtransitionintime,fromtheshortertime‐
range,regionalforecastmodelstotheglobalmodelwithlongerforecastrangeareapplied.Thesetofparameter
requiredforSearchandRescueoperationsincludeseasurfacetemperatureandcurrents,
wavesandwinds.The
currentversionoftheaggregationmethodwasdevelopedforsurfacetemperatureandsurfacecurrentsbutit
will be extendedto waves in latter stages. The method relies on the calculation of aggregation weights for
individualmodels.Forseasurfacetemperature(SST),nearreal‐timesatellitedataat
clear‐skylocationsforthe
pastdaysisusedtodeterminetheaggregationweightsofindividualforecastmodels.
A more complicated method is to use a weighted multi‐model ensemble (MME) approach based on best
forecast features of individual models and possibly including near real time observations. The developed
method
exploreshowsatelliteobservationscanbeusedtoassessspatiallyvarying,nearrealtimeweightsof
differentforecasts.Theresultsshowedthat,althoughaMMEbasedonmultipleforecastsonlymayimprovethe
forecast,iftheforecastsareunbiased,itisessentialtouseobservationsintheMMEapproachsothat
proper
weightsfromdifferentmodelscanbecalculatedandforecastbiascanbecorrected.Itisalsonotedthat,insome
months,e.g.,June inBalticSea,evenSSTwasassimilated,theforecaststillshowquitehigherror.Therearealso
visible difference between different Copernicus Marine Environment Monitoring Service
(CMEMS) satellite
products, e.g. OSTIA and regional SST products, which can lead different forecast quality if different SST
observationproductsareassimilated.
http://www.transnav.eu
the International Journal
on Marine Navigation
and Safety of Sea Transportation
Volume 17
Number 3
September 2023
DOI:10.12716/1001.17.03.04
534
Baltic Sea,North Sea, MediterraneanSea, Black Sea,
Norwegian Sea and parts of Atlantic and Arctic
oceans (see Figure 1), for coordinated maritime
activities such as search and rescue operations and
planning. For the FRONTEX search and rescue
service, the forecast period is required to be seven
dayslongand
updatedfourtimesperday.Currently,
noneofthecommunityornationalforecastservicesis
able to meet this requirement. Global forecasts
produced by organizations like Copernicus Marine
Environment Monitoring Service (CMEMS),UK Met
Office and CMCC (Euro‐Mediterranean Centre for
Climate Change), cover the pan‐European seas, but
they
areonlyupdatedonceaday,andtheirforecast
skills have not been specifically tuned for the
European seas. Regional oceanographic forecasts,
both from national and CMEMS forecast services,
havehigherresolutionandupdatefrequencybutthey
typically cover only part of the European seas, and
their forecast ranges sometimes are
less than seven
days. Therefore it is necessary to combine different
oceanographicforecaststogenerateaEuropeanwide,
qualityensuredmodelproductthatmeetsalltheuser
needs.Alltheimportanthydrodynamicquantitiesfor
the operations, such as sea surface temperature and
currents,shouldhaveseamlesstransitionbetweenthe
different
seasandoceanographicareas.
There are two ways to make this seamless
EuropeanSeaforecast.Oneisusingstaticweightsthat
ensureasmoothtransitionbetweenregionalproducts,
the other is using dynamic weights to aggregate
products from different models to a Multi‐Model‐
Ensemble (MME) product. The first method uses
smooth, static spatial weighting functions for the
individual forecasts to aggregate them smoothly at
the boundaries of the forecasting area. Since some
forecasts have ranges shorter than seven days, a
temporal smoothing should also be performed. To
generate seamless transition in space and time,only
one forecast isneededfor
a given region.Hence for
eachregionandupdatetime,a“bestforecast”should
be selected. This approach is referred as simple
aggregation.
Amorecomplicatedmethodistouseaweighted
multi‐modelensemble(MME)approachbasedonbest
forecast features of individual models and possibly
including near real time
observations. Such kind of
method has been developed in the atmospheric
science [1,2, 3]showing improvedforecasts [4]. For
oceanforecasting,theMMEapproachhasbeenused
togeneratesealevelforecastattidegaugestationsin
the Baltic‐North Sea. For ocean field forecast, the
MMEforecasthas
appliedsameweightsfordifferent
models, instead of using observations to determine
models’weights[5].
In this paper, both approaches will be
implemented. The simple aggregation method has
been set‐up to perform operational forecasts. The
MMEaggregationwasdevelopedtoreplaceit,andis
currently available for SST forecasts in
the Baltic‐
NorthSeasaswellasinMediterraneanSeaandBlack
Sea, where it has been implemented, tested and
validated. The developed method explores how
satellite observations can be used to assess spatially
varying,nearrealtimeweightsofdifferentforecasts.
The paper is organized as follows: section 2
describes methodology and input data, section 3
analysesresultsandsection4isconclusions.
2 METHODANDINPUTDATA
This study focus on examining feasibility of using
Copernicus Marine Environment Monitoring Service
(CMEMS) and national forecasts, both global and
regional,formakingapan‐EuropeanSeaaggregated
forecast. The aggregation forecast
experiments are
madeandassessedfortwoperiods:a7‐monthperiod
duringSeptember3,2022–March15,2023including
allforecastswithfocusingonthegeneralperformance
of the method, and a one year period from May 1,
2021 – April 30, 2022, with focusing on seasonal
variability.
However,onlyCMEMSandDMIforecasts
areusedinthisperiodasCMCCglobalproductisnot
availableforthisperiod.
2.1 Inputdata
BothmultipleforecastproductsofSSTandseasurface
currentsandsatelliteSSTobservationsareusedinthis
study.
2.1.1 Forecastproducts
Theforecastproductsusedin
thisstudyconsistof
global forecast from CMEMS and CMCC, and
regionalforecastfromCMEMSandDMI.Asummary
oftheproductsisshowninTable1.
DMI product DKSS uses sub‐domains of higher
resolutionintheDanishstraits.
Thereareafewthingstonoteaboutthedifferent
forecastproductsthatareusedintheaggregation.
Dataassimilation:AllforecastsinTable1useSST
dataassimilationexcept for DMIforecast.Therefore,
all the forecast products except DMI’s may feature
smallertemperaturebias.Itshouldalsobenotedthat
global and regional model systems assimilating
different SST products, for
example, CMEMS global
forecast assimilates OSTIA L4 SST while most of
CMEMSregionalforecastsystemassimilatesregional
L3S SST. Thedifferences in the OSTIA and regional
SSTdatawillaffecttheweightsofdifferentforecasts
intheMMEforecastaggregation.
Currents:allregionalforecastshavetidesincluded
in the model,
except for the two global forecast
products (CMEMS, CMCC). In order to obtain the
totalcurrentsfromtheglobaloceanographicproducts,
separateforecastsoftidalcurrentsareobtainedfrom
CMEMSglobalproduct.
Some areas not covered by the CMCC (Euro‐
Mediterranean Centre for Climate Change) global
product like inland partsof
fjords are excluded also
from CMEMS global forecast. CMEMS
Mediterranean,CMEMSBlackSeaandCMCCglobal
forecasts do not cover Marmara Sea, Azov Sea, the
narrowDardanellesStraitattheeasternpartbutthey
arestillcoveredbyCMEMSglobalforecast.
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Table1.Individualforecastproductsusedforaggregationforecast(SSTandsurfacecurrentsonly)
___________________________________________________________________________________________________
AreaProviderSpatialTemporal Update Forecast
resolution resolution time(h) range
___________________________________________________________________________________________________
48‐66N,4W‐30EDMI(Baltic‐NorthSea)0.05deg.Hourly 00,06,12,18 5days
11‐73N,43W‐43ECMEMS(Global)0.083deg. Hourly 12 10days
46‐62.75N,16W‐13ECMEMS(NWShelf)[6]0.03deg.Hourly 12 6days
26‐56N,19W‐5ECMEMS(BayofIberian‐Biscay‐Ireland)
0.028deg. Hourly 12 5days
53‐66N,9‐30ECMEMS(BalticSea)0.018deg. Hourly 00,12 6days
30.18‐45.98N,17.29W‐36.30E CMEMS(MediterraneanSea)[7] 0.042deg. Hourly 12 5days
40.5‐47.0N,27.25‐41.1ECMEMS(BlackSea)[8]0.025deg. Hourly 12 5days
11‐73N,43W‐43E
CMCC(Global)0.0625deg. Hourly 12 6days
___________________________________________________________________________________________________
Eastern part of Atlantic Ocean is covered by
CMEMS regional Iberian‐Biscay‐Ireland (IBI) model.
It is not yet implemented in the operational
aggregatedforecastproduct,butitisincludedinSST
validation results in order to estimate whether to
includeitinupdatedoperationalaggregation.
2.1.2 SatelliteSST
RegionalSST
satelliteobservationsofLevel3from
CMEMS are preferred for forecast aggregation in
regional seas, i.e., Baltic Sea, North Sea,
MediterraneanSeaandBlackSea.ThisincludesNorth
Sea/BalticSea‐SeaSurfaceTemperatureAnalysisL3S
product, Mediterranean Sea‐High Resolution and
Ultra High Resolution L3S Sea Surface Temperature
product [9],
Black Sea‐High Resolution and Ultra
High Resolution L3S Sea Surface Temperature
product [9], andCMEMS global Level 3 product. In
the areas where Level 3 SST is not available in
CMEMS,e.g.,inthe Arctic Ocean and Atlantic open
sea, Level 4 SST from CMEMS SST Thematic
Assembly Center (TAC)
is used. As a consequence,
CMEMSArcticLevel4[10]productiswellsuitedfor
theArcticarea.
ModelledSSTaswellassurfacecurrentsdepends
onthethicknessofupperlayerusedinthemodel.In
general, regional models have higher vertical
resolution and thus SST could be resolved
better.
Observed SST of weather satellites often relates to
nearsurfacepartoftheseasurfaceandistypicallyat
lower depth than the first layer depth of a forecast
model. Some of CMEMS SST Level 3 observation
products have both SST and adjusted SST as
Mediterranean Sea, Black Sea and
global ocean
products. Adjusted SST observations have a lower
influencefromdailySSTvariationsandareusedfor
validationoftheindividualmodelshere.SSTsatellite
observations are often stated as daily average value
but depend on exact timing of pathing satellites in
theirorbits.Therefore,SSTobservationscomewith
its
natural deviations which are typically lower than 1
degreeoftemperature.
SatelliteSeasurfacetemperatureproductsareused
for the calculation of dynamic and static MME
aggregation weights. Sea surface temperature is one
of the best products that satellite monitoring can
deliver for the oceanographic conditions. Existing
regional SST satellite
observations are better
parametrized for corresponding seas: North Sea,
Baltic Sea, Mediterranean Sea, Black Sea and Arctic
Ocean. Therefore, global SST observations are used
onlyinareasoutsidetheregionalones.CMEMSSST
observations of Level 3 type are used everywhere
excepttheArcticwhereLevel4satelliteobservations
are
used. Level 4 observations in Arctic Ocean are
filtered in such a way that only observations with
standard deviation between 0.001 K and 0.2 K are
selected, that approximately corresponds to valid
Level 3 observations. Observations with existing ice
maskareexcludedastheseSSTobservationsmaybe
lessaccuratein
thissituationthanthemodelledresult.
2.2 Simpleaggregationmethod
To obtain an aggregated forecast, the simple
aggregation method is used to smoothly merge
multiple forecasts with different spatiotemporal
resolutions and coverages into a unified grid,
coverage and forecast range. This aggregation
involvesseveralstages.
First, spatial and temporal grid
is constructed to
covertheforecastarea(11°N ‐73°N,43°W‐43°E)
withtherequestedresolutionof0.1degree,anda7‐
dayforecastperiodwithanhourlyinterval.Thatgrid
actsasthebasisfortheaggregationmethod,andthe
aggregated product with the specified grid is
deliveredtoFRONTEXusers.
Next,a commonland‐sea maskisconstructedon
thebasegridtoensurethesamerepresentationforall
forecastproducts.Disconnectedsmallwaterbodiesin
thebasegridareremoved,andmostofinlandfjords
arealsoremovedastheyarerepresentedonlyinone
ortwoforecastproducts.TheCMEMSglobalproduct,
withaspatialresolutionof0.083degreeandthebest
spatialandtimecoverage,isusedasthebasisforthe
land‐seamaskinordertoensurethatallgridpoints
arerepresentedfortheentireforecastperiod.
Then,aweightingfunction
isconstructedforeach
forecast source on the base grid to ensure smooth
transitioninspaceandtime.Spaceandtimevariables
are separated in the weighting function for each
forecastsourcei:
,, ,
iii
w lat lon t g lat lon h t
(1)
wherelatislatitudeandlonislongitude,andtistime.
The spatial function g
i(lat,lon) has a transition zone
around the boarders where regional and global
forecasts overlap. This ensures continuous spatial
transitionfromaregionalsolutiontoaglobalone.A
scalingcoefficientaiisaddedtoputahigherweight
onaregionalforecastsource:
Thenextstepistoperformalinear
interpolationof
source forecast fields from their model grids to the
base grid. Each variable (SST and components of
surface currents) of each model source results in
536
separate interpolated field. However, linear
interpolationdoesnotworkatcoastallocations,soa
nearestneighbourmethodisused,andifitfailstoget
a value, then a moving average is selected with a
windowsizenotexceeding0.3degrees.Afterthat,the
common land‐sea mask is applied
to cut off
unnecessary points, and NAN (not any number)
valuesareusedoutsidetheareacoveredbyasource
forecast.
Then,aweightingfunctionisconstructedforeach
sourceonthebasegridtoensuresmoothtransitionin
space and time. Space and time variables are
separatedinthe
weightingfunctionforeachforecast
sourcei:
,, ,
iii
w lat lon t g lat lon h t
(2)
where lat is latitude and lon is longitude, t is time.
Weighting function is not normalized at this stage.
Thefinalweightsarederivedwhenallthesourcesare
considered.Thespatialfunctiong
i(lat,lon)hasabuffer
zoneinopenwatersfortheregionalforecastsources
toensurecontinuousspatialtransitionfromaregional
solution to the global one. A constant scaling
coefficient ai is added to put a higher weight on a
regionalsource:
,,
iii
g
lat lon a lat lon
(3)
where weighting function η
i(lat,lon) of forecast i
changesfrom0to1,seeFigure1.Ifitis0,thesourceis
disregardedatthegivenlocation,andif it is 1,then
thereismaximaleffectofthecorrespondingsourceon
the aggregated product at the given location.
Coefficients a
i are chosen according to validation
resultswhicharetypicallybetterforregionalforecast
sourceswithhigherresolution.
Figure1. Blue rectangle‐area of aggregation. Shaded
rectangles: unit weighting function η
i(lat,lon) for regional
modelareas (NorthwestShelfSea,BalticSea,Mediterranean
Sea,BlackSea)
Mostofthesourceshaveaforecastperiodofless
than seven days. Therefore, time function h
i(t) is
constructed,whichis1whenthecorrespondinghour
iscoveredinthesourceforecastand0whenitisnot.
However,thiswouldresultinstep‐likejumpintime.
Hence, function h
i(t) is chosen in such a way that it
continuouslychangesfrom1to0atthefinaldayof
theperiodcoveredbyforecastsourcei.
Ifaspecificforecastsourcemaynotbeavailable,it
isdisregardedbysettingitsweightingcoefficienta
ito
zero.Finally,avalueV(lat,lon,t)inaggregatedforecast
productisobtainedfromcombinedvaluesv
i(lat,lon,t)
ofweightedsourcesonthebasegrid:
,, ,,
,, ,
,,
ii
i
ii
i
i
v lat lon t w lat lon t
V lat lon t g lat lon h t
wlatlont
(4)
wheresummationoccursoversourceswithnon‐NAN
values. The V value can represent any scalar value,
e.g.,SSTorcomponentsofthesurfacecurrents.
2.3 Multi‐Model‐Ensemble(MME)aggregationmethod
SST forecasts are typically accompanied with daily
satellite SST observations from the preceding days,
allowing for the
minimization of forecast bias.
Furthermore, multiple forecasts are available for a
given region, such as global and regional forecasts
fromCMEMSandnationalservices.Thispresentsthe
potential toimprove SSTforecastbeyondthesimple
aggregation method by using a MME aggregation.
SatelliteSSTobservationsenabletothedetermination
of optimal
weights for individual forecasts in the
aggregatedproduct. Insuchacase,onewouldoften
expect that regional oceanographic forecasts will
outperform the global ones. As a result, higher
weights are assigned to the regional products. The
MME aggregation will not be applied to locations
withicemasks.
Forthe
MMEaggregation,thefirststepistoobtain
theforecasterrorstatistics.Thentheforecasterroris
used to calculate the weights for different forecast
productsandfinallytheMMEaggregatedforecastis
obtainedasalinear,weightedsumoftheindividual
forecasts. SST deviation at location‐time (x,t) of a
forecastiis:
0
,,,
ii
Txt Txt T xt
(5)
whereT
0(x,t)issatelliteSSTateachgridpointx=(lat,
lon)andtimemomentt.T
i(x,t)ismodelledSSTvalue
oftheforecastmodeli.
Inthesameway,squaredtemperaturedifferenceis
treated.Mean square differenceat location‐time (x,t)
offorecastiis:
2
2
0
,, ,
ii
Txt Tx xt tTx xt t
(6)
Inordertohavespatiallyand temporallysmooth
squarederrordistribution,rollingmeanvalueisused
ateachgridpointxandtimet:
2
2
,0
,
1
,,,
m
irol i
xt
Txt TxxttTxxtt
m
(7)
where,inpractice,∆xrunsthrough5×5spatialgrid
pointsoflatitudeandlongitudecentredongridpoint
x;∆trunsthrough7days:‐3days,‐2days,….,3days
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centredoncurrentdayt;m=5× 5×7=175.Points
with no data values at location‐time x+∆x,t+∆t are
excludedfromaveraging.
Using multi model ensemble, local weighting
factorforeachsourceiisobtainedby:
4
2
,
,
4
2
,
,
,
,
irol
irol
jr
j
ol
Txt
wxt
Txt
(8)
The4
th
powerisusedhere,inordertohavehigher
weightforthebestproduct.Forthesamereason,bias
isnotsubtractedatthisstage.Theresultingdeviation
at(x,t)ofmulti‐modelensembleis
,
,,,
irol i
i
Txt w xt T xt
(9)
wheresummationoccursoverallforecastsourcesiin
the area. The resulting centred Root Mean Square
Error(cRMSE)at(x,t)ofmulti‐modelensembleis
22
,
,,,,
irol i
i
cRMSE xt w xt T xt T xt
(10)
These formulas yield quantitative estimations of
qualityofeachforecastsourceandresultingeffecton
theaggregatedproduct.
Figure2.Left:CountofLevel3observationsfromregional
andglobalCMEMSsourcesateachlocationon0.1×0.1grid
in September 3, 2022 to March 15, 2023. Right: bias of
weightedproduct(9)of3forecastmodels:CMEMSglobal,
CMCCglobalandCMEMSregional.
Figure3. Left: weight of CMEMS regional product (Black
Sea,MediterraneanSea,BalticSea,NorthWestShelf,Iberia
BiscayIreland)withrespecttothesetof3forecastmodels:
CMEMSglobal,CMCCglobalandCMEMSregional.Right:
weightofCMCCglobalproductinthesameconfiguration
Figure4. Left:central RMSE of combined set of 3 forecast
models: CMEMS global, CMCC global and CMEMS
regional (Black Sea, Mediterranean Sea, Baltic Sea, North
West Shelf, Iberia‐Biscay‐Ireland). Right: central RMSE of
onlyCMEMSregionalproductinrespectiveareas
3 RESULTS
Results of the Multi‐Model‐Ensemble (MME)
aggregation method of have been analysed for 2
periods covering different data products. The first
experiment 09/22‐03/23 includes all regional and
globaldatasets,butdoesnotcoveranentireyear.The
second experiment 2021‐2022 includes all regional,
but only
one global data set,the CopernicusMarine
Environment Monitoring Service (CMEMS) global
productandcoversonefullyear.Itcanthereforebe
usedfortheassessmentoftheseasonalvariationsof
the MME aggregation method. Finally, the
operationalimplementationofthesimpleaggregation
methodusingstaticweightsisdiscussedas
well.
3.1 Experimentduring09/22‐03/23
Thefirstexperimentstudiesthespatialpatternofthe
MME aggregation on European scale. It covers a
limited time frame of 7 months (September 2022 to
March 2023), because CMCC (Euro‐Mediterranean
Centre for Climate Change) global data was not
availablefortheperiodprior
to09/23.Figure2shows
thenumberofobservationsintheconsideredperiod
September2022toMarch2023.Thehighestnumberof
clear‐sky dayswithvalidSSTobservationsoccursin
Mediterranean Sea, Red Sea, at latitudes of around
25oN. CMEMS regional SST observations in North
Sea, Baltic Sea and
Arctic Ocean provide higher
number of days with valid observations. Lowest
numberofobservationsoccursinAtlanticsatlatitude
of 50 degrees due to the specific positioning of the
satellite orbits. Also, Arctic coastline has lower
number of observations due to ice mask in winter
time.
Figures 3‐4 show derived
weight of CMEMS
regional or CMCC global forecasts (Figure 3) and
central Root Mean Square Error (cRMSE, Figure 4)
when3forecastsareinvolved:CMEMSglobal,CMCC
global and CMEMS regional. CMEMS regional
forecast model corresponds either to Black Sea,
Mediterranean Sea, Baltic Sea, North West Shelf
(NWS) or Iberia‐
Biscay‐Ireland model. Iberia‐Biscay‐
Ireland model is not yet included in operational
aggregationbutincludedinvalidationresults.Biasof
weighted product (9) is well within half a degree
range,seeFigure2right.Thatbiasiseasilyremovable
fromthefinalproduct.
538
CMEMS regional models clearly dominate the
weights in the aggregation in the North West Shelf
and Black Sea, see Figure 3. Actually, some of the
models like North West Shelf (NWS) model benefit
from the fact that it uses best‐estimate products for
thedayspriortotheanalysisthat
incorporatealsosea
surface temperature (SST) observations. These data
arethenstoredinhistoricalCMEMSdatabasethatare
used for validation. For this reason, the real
operational NWS forecast product from CMEMS is
notasaccurateasthehistoricalNWSdatasetarchived
atCMEMS.Henceforth,thecalculatedMMEweights
that
use historical data do not necessary reflect the
qualityoftheforecastdata(Figure3).
Regional Baltic Sea model has good performance
in SST, but may slightly over‐predict upwelling
eventswhicharerathertrickytomodelinBalticSea,
see Figure 5. Also, locations with upwelling events
maypromotecreation
oflowaltitudecloudsmeaning
that usable satellite SST observations may not be
available. Mediterranean and Iberia‐Biscay‐Ireland
regionalmodelsshowapproximatelythesamequality
withrespecttoSSTobservations.Mediterraneanand
Black Sea models use 3DVAR scheme of OceanVar
[11] that assimilates data predominantly in weekly
basis. Different
assimilation scheme can lead to that
SST performance sometimes falls behind CMCC
global oceanographic model as in the given time
periodof7months.
Figure 4 shows that cRMSE of the weighted SST
product of the mentioned 2 global models and 1
regional model in the respective sea. The result is
better inNorth West Shelf and Black Sea wherethe
weight of regional product dominate. The first one
may benefit from hindcasting nature of North West
ShelfarchiveddatainCMEMSdatabase.Bothofthe
global modelling productsare less effective in Black
Seathatleadstodominanceofthe
regionalBlackSea
product. Some larger deviations occur at Gibraltar.
Also the Mediterranean and West African coastlines
havealowercombinedaccuracythatmayresultfrom
ability of Nemo oceanographic model to handle
shallowerwaters.ThereisstronggainofusingMME
inMediterraneanSeaandBalticSearatherthanusing
theCMEMSregionalproductalone,compareFigure4
leftandright.
Thequalityoftheaggregatedproductdeteriorates
astheforecast becomes longer.It is because thereis
lower number of models for the final days and the
performanceofthemodelsdecreaseswithincreasing
forecast length in general. Validation
results in [12]
suggest that relatively good results are obtained for
thefirst3‐4daysoftheforecast.Thefinaldaysofthe
forecast can be used only as initialestimate of what
conditions are expected without a remarkable
accuracy.LongerforecastsofSSTaregenerallymore
accurate than that
of the currents, because
temperature is essentially a cumulative quantity of
resultingfrompreviousconditions.
Figure5.ExampleofSSTtimeseriesof3differentforecast
modelsandobservationsinBalticSeanearSwedishcoastat
latitude=58.4°andlongitude=17.3°
3.2 Experimentin2021‐2022(Seasonalvalidationof
SST)
Seasurfacetemperaturefeaturesastrongseasonality
at northern latitudes. In winter, the SST is close to
zerodegrees with verysmall day to day changes as
wellassmalldiurnalvariations,whereasinsummer,
SSTfeaturesstrongdaytodayvariations
withdistinct
diurnalcycle.Figure6showsmonthlycRMSEofthe
aggregated MME forecast. It is noted that there are
exceptionally high forecast errors in June and July,
which is originated from all the individual forecast
(Figure 7). Consequently, optimal weight of each
sourcemodelintheaggregationcoulddepend
onthe
season. For example, monthly weight of CMEMS
Baltic Sea model is dominant in spring‐summer but
less dominant in autumn, seeFigures 6 ‐7. The main
reason why CMEMS regional Baltic Sea model has
less accuracy in autumn months is a slight over‐
prediction of upwelling events resulting in
a high
penalty. Also in Mediterranean Sea, the CMEMS
regionalproductisbetterinsummerandspring,but
itprovideslessaccuracyinautumn,seeFigure7.
Figure6.MonthlyweightedcRMSE inBalticSeainperiod
fromMay2021toApril2022.Theincludedforecastmodels
are CMEMS global, DMI DKSS and CMEMS Baltic Sea
model.
539
Figure7.MonthlyaveragedRMSEofSSTinregionalseasof
CMEMSregional(NorthSea,BalticSea,MediterraneanSea,
BlackSea)model,DMIDKSSmodelforNorthSea‐BalticSea
(upper row) and CMEMS global ocean model and the
weighted model. RMSE and cRMSE represent weighted
valuesofaggregatedproduct.
Figure7showsmonthlyRMSEinregionalseas.In
general,itislessthanhalfadegree.Itisslightlyless
inwinterwhentypicalvariations of temperatureare
lower. The CMEMS regional products clearly
dominate here. Use of MME still improves the final
result, especially in Mediterranean Sea. CMEMS
regional
product in Mediterranean Sea has larger
deviationsinmonthsofautumn.Figure7alsoshows
thattheaggregatedMMEproductfeaturesthelowest
RMSEvaluesinallregions.
Figure8. Seasonal bias (in degrees) of SST regional seas:
NorthWestShelf,BalticSea,Mediterranean SeaandBlack
Sea. The included models are CMEMS global model,
CMEMSregionalmodel inrespectiveareaandDMIDKSS
modelinNorthSea–BalticSea. Thebluelineisbiasofthe
weighted
product(9).
Figure 8 shows seasonal bias in regional seas.
NegativebiasistypicalinNorthWestShelfandBaltic
Sea.TheCMEMSregionalproductsclearlydominate
here, too, as they extensively use SST assimilation
scheme.Theyhavemostnegativebiasinwinterwhen
thenumberofclear‐skydaysislowestand
thereisa
smaller amount of satellite SST data available for
assimilation.TheDKSS model isnotusing SST data
assimilation.Forthisreason,theSSTbiasoftheDKSS
model is higher. Thus, the bias of the aggregated
product is very close to CMEMS regional product,
which is having
a larger weight. CMEMS regional
productinMediterraneanSeahasmonthlybiaswith
amplitude less than 0.1 degree that results from the
fact that a larger amount of satellite SST data is
available for data assimilation (Fig. 2). CMEMS
regional product in Black Sea uses similar model
parameterisation as in Mediterranean
Sea but has
pronouncedpositivebiasinsummer.
3.3 SSTbiascorrectioninaggregatedforecasts
The validation results showed that resulting bias of
SSTtakingintoaccountseveralmodelsisusuallyless
thanadegreeinregional seas.Theweighted bias of
aggregated product shown in Figure 2 right and
Figure 8 can be subtracted from the final result. It
means that SST observations can be used to correct
thebiasesofthemodeldata.However,thenearreal
time SST observations and model forecasts do not
overlap in time. Therefore, aggregated forecast data
are archived for the past 3 days
which are then
comparedtoSSTobservationsofthesamedays.This
yieldsaninitialestimationofthelocationdependent
bias correction function ∆
o(x) for the start of the
forecast. Because, it is unclear how the bias could
change on the forecast then the amplitude of initial
biasisgraduallysettofadeforthe finaldays of the
forecast. The time dependent fading factor is set to
haveanexponentialdecrease
/
,
t
o
xt x e
(11)
where τ is 3 days. Bias correction is set to zero in
locations masked as cloudy or with an ice mask.
Moving average method is used to obtain a smooth
biascorrectionfunction∆
o(x)withspatialwindowof
0.5degrees.
Regarding optimal weight maps for the
operationalforecasts,wecannotuseadetailedtime‐
dependentweightmapsasinFigure4becausethere
are no SST observations in forecast period. Instead,
optimalsetofweightsofindividualmodelsourcesare
derivedfromvalidationresults
ofhistoricaldata.
3.4 Operationalimplementation
Thecoreprocedureofaggregationiscarriedoutina
Python script using Xarray module to work with
gridded NetCDF or Grib data. The script has been
running operationally four times a day since
November 2021 at Danish Meteorological Institute
(DMI).Theperformanceof
theoperationalproduction
is monitored in real time using an automatic
monitoring tool. If there are errors in downloading
and aggregation, a warning will be sent to assigned
forecasters with an error report. An example of
aggregatedSSTisshowninFigure9.Ascanbeseen,
seamlessspatialtransitionfrom
regionalsolutionsto
global ones is well represented. Also transitions in
timearesmooth.
540
Figure9. Example of operationally aggregated SST at
2023.04.1100:00:00usingMME.LeftisSSTatthestartofthe
forecast, right is SST development in time at selected
locationsshownbylatitude,longitudevaluesinlegend.
4 CONCLUSIONSANDDISCUSSIONS
Inthisstudy,aggregatingmet‐oceanforecastforpan‐
European seas is implemented and validated by
integratingCMEMSandnationalglobalandregional
forecasts, using both a static‐weight deterministic
method anda MME‐based dynamicweight method.
Inthestatic‐weightmethod,continuoustransitionin
space
and time between different models is made
using spatial weighting functions with gradual
transitionsinspaceinordertoproduceafourtimesa
day,pan‐Europeansea7‐dayforecast.Inordertotest
theperformanceofaggregatedforecast,validationof
SSTisused.IntheMME‐basedmethod,
theSSTerror
statisticsareusedtogenerateoptimalweightsofeach
individual forecast model. Based on one year
verification results, regional oceanographic models
outperform the global ones as they have a higher
nativeresolution.Itshouldbenotedthatsomeofthe
regional models use a strong hindcasting nature of
archived data in CMEMS database, e.g., CMEMS
North West Shelf model that leads to very good
performance for historical dataset but not necessary
for the forecast. CMEMS Baltic Sea model uses SST
assimilation, but slightly overestimates upwelling
events near coastline in autumn. Similarly, CMEMS
Mediterranean model has a good performance
with
respect to SST through almost all ofthe yearexcept
autumn, when CMCC global oceanographic model
providesbettervalidationresults.Itmayresultfrom
assimilationschemeinCMEMSMediterraneanmodel
whichisrunningonaweeklybasisratherthandaily
one.Inordertoobtainsmoothweightingfunction,a
moving
average error analysis is made with small
special window. That yields a weight map showing
the strong and weak areas for each of the forecast
model. That is used to estimate the weights in the
operational version. MME approach yields notable
benefits over simple aggregation method. It is
especiallynotable
inareaswhereasinglemodelisnot
dominating as in Mediterranean Sea. The same
principles of aggregation will be used also for
aggregation of other fields as surface currents and
waves.
It was found that, in the Baltic‐North Sea,
individualmodelshaveveryhigherrorsinJuneand
July
even if SST has been assimilated. The situation
can be improved by using MME based aggregation
butstillgivehigherrors.
The aggregation method of forecasts should be
robustandworkevenifsomeoftheforecastmodels
are missing at the time of aggregation. Therefore,
multi‐modelensembleis
essentialtoreplaceamissing
model withthe other ones. Moreover, some forecast
models may beoutdated atthetime ofaggregation.
These situations are handled by proper selection of
dynamic weights of the individual models in the
aggregationmethod.
Majordifferencesofthesemodelswithrespectto
observations occur in
autumn and winter when the
skies are cloudier and the amount of data and data
quality are both low. Moreover, upwelling events
havegenerallylowerforecastaccuracyandaremore
characteristicinautumn.Therefore,itisexpectedthat
there could be major deviations of modelled SST in
autumnandwinter
months.
ACKNOWLEDGEMENT
This study is supported by FRONTEX project
“Frontex/OP/234/2021/RS Meteorological and Oceanic
ServicesLot2‐OceanographicDataandVisualisation”.The
authors acknowledge to Rita Lecci and CMCC colleagues
forprovidingCMCCglobalforecastproduct.
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