the generalized flather lateral open boundary...
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ThegeneralizedFlatherlateralopenboundarycondi5on
P.Oddo(1)andN.Pinardi(1,2)(1)INGV,Bologna,Italy
(2)Dept.ofEnvironmentalSciences,Univ.ofBologna,Italy
Sub‐5tle:Theneedofopera5onaloceanographyforincreasedforecastskillnearthe
coasts
Outline
1. Opera5onalOceanographyandthenes5ngapproach
2. Thenes5ngconundrum:theLateralBoundaryCondi5onproblem
3. ThegeneralizedFlatherboundarycondi5ons4.TheCoastalRapidEnvironmentalAssessment
(CREA)methodology:apossibleframeworkfortes5ngstructured/unstructuredgridmodels
Multidisciplinary Multi-platform Observing system (permanent and relocatable)
Numerical models of
hydrodynamics and ecosystem,
coupled a/synchronously to atmospheric
forecast
Data assimilation for optimal field
estimates and
uncertainty estimates
Continuos production of nowcasts/forecasts of relevant environmental state variables
The operational approach: from large to coastal space scales (NESTING),
weekly to monthly time scales
OBSERVING SYSTEM
MODELING SYSTEM
MOORED BUOY ARRAYS SOOP EXPANDABLE AND ONDULATING INSTRUMENTS SATELLITE SENSING: SEA LEVEL, SEA SURFACE TEMPERATURE, SEA SURFACE SALINITY, COLOR, WINDS DRIFTING BUOYS (SURFACE AND SUBSURFACE) GLIDERS
REPEATED MULTIPARAMETRIC SECTIONS SATELLITE AND AERIAL SURVEYS COASTAL RADARS AUTONOMOUS UNDERWATER VEHICLES CABLED MULTIPARAMETRIC STATIONS RIVER RUNOFF AND LOADING MONITORING SEDIMENT/WQ MONITORING
MODEL PHYSICS PRIMITIVE EQUATION (> 1-5 KM) TURBULENCE CLOSURE SUBMODELS
MODEL PHYSICS Non-Hydrostatic (<1- 5 KM) TURBULENCE AND LIGHT
SUBMODELS
DATA ASSIMILATION OPTIMAL INTERPOLATION 3-DVAR, KALMAN FILTER
DATA ASSIMILATION KALMAN FILTERS ADJOINT MODELS
BIOCHEMICAL MODELS PELAGIC COMPARTMENT BENTHIC CLOSURE
BIOCHEMICAL MODELS PELAGIC COMPARTMENT
BENTHIC-PELAGIC COUPLING SEDIMENT DYNAMICS
ATMOSPHERIC FORCING OPERATIONAL ANALYSES AND FORECASTS FROM LARGE SCALE MODELS
ATMOSPHERIC FORCING OPERATIONAL ANALYSES AND
FORECASTS FROM LIMITED AREA MODELS
Whynes5ng?• Increasetheresolu5onwhereusersneedit(especiallycoastalusers)
• Opera5onaloceanographyproductsgivebasicfirstguessfieldsforhighresolu5oncoastalmodels
• Nes5ngallowstheintroduc5onofnewphysics(haveresolu5onANDPROCESSESwhereandwhenyouneedthem,Robinsonetal.,1998)
• Prac5calandincrementalwaytoimplementnewtechnologyintheopera5onalframework
The European Operational Oceanography Service 6 European Seas + Global Ocean
Every day the ocean weather with uncertainty estimates
Ocean Core Information – Temperature, Salinity,
Currents, Color, Sea Level, Ice variables, Bio variables
– Hindcast, NowCast, Forecast
– Re-analyses
One single desk – access point to the MyOcean pan-
european information
Open Data Policy – Open access – Free access
Theopera5onalforecas5ngmodelsnow
• Primi5veequa5onsinsphericalcoordinateswithfulloceanthermodynamics
• Physics:– Subgridscaleparametriza5onsforhorizontalviscosityanddiffusivity
(fourthandsixthorderlaplacians)– Highfrequencyatmosphericforcingandadvancedair‐seainterac5on– Turbulenceclosuresub‐modelsforthever5calviscosityanddiffusivity– Bo_omboundarylayerparametriza5ons– Tidalpoten5alincluded– Surfacewave‐currentcoupling
• Dataassimila5oncomponents:mul5variateschemesassimila5ngallavailabledatainreal5me(satelliteandinsitu)
• Simplifiedphysicsforecas5ngmodels:– shallowwatermodelsforstormsurgeforecas5ng– Wavemodelsforsurfacewaveforecas5ng
MOM1.1+SOFAOPA8.2+SOFA(sys2b)OPA8.2+3DVAR(sys3a2)NEMO+3DVAR(sys4a)
rmse
1999
2009
SEALEVELintheMEDSEA
Theerrorsofstructuredgridmodels(pasttenyearsofdataintheMediterranean)
nbofSLADATA nbofTemperatureDATA
RMSEofSLA RMSEoftemperatureat8m
EuroGOOSConference,Exeter,2008Athens,MemberAssembly,4‐5March2008
Shelfandsub‐regionalmodelsnowreach1‐3kmresolu8on
TheMediterraneanForecas8ngsystemdisseminatesdailyforecaststo13nestedna8onalmodelseveryday
Opera5onalOceanography:thenes5ngdeluge(allstructuredgrids)
Opera5onaloceanographyNes5ngwithunstructuredgrids:SHYFEM3‐D
CoastalModelstartedfromShelfmodel
Analysisoflandsourcesofpollu5onandtheirimpactInthesea
Bellafioreetal.,2010
Op.Oc.nes5ngissueswithstructuredandunstructuredgrids
• Ini5aliza5onproblem:ini5alizingallprognos5cstatevariablesfromthecoarsetothehighresolu5ongrid.VIFOPdeveloped(Varia5onalIni5aliza5onandForcingPlaeorm,Auclairetal.,1999,2000,2006)butmoreisneeded(mass‐conservinginterpola5ontools)
• Ver5calBoundaryCondi5onproblem:higherresolu5onatmosphericforcingusedinthenestedmodel,needforconsistency(?)
• LateralBoundaryCondi5onproblem:delicateproblem,wefocusedonthat
TheLateralBoundaryCondi5onproblem
• Mainlysolvedinthe70’sforlimitedareamodels• Barotropicquasigeostropicequa5onsareill‐posed(Benne_
andKloeden,1978)butforshort5mescaleserrorscanbekeptbelowathreshold(RobinsonandHaidvogel,1978)
• Primi5veequa5onsforatmosphere(OligerandSundstrom,1978,Orlansky,1976,MiyakodaandRosa5,1977)
• Primi5veequa5onsfortheoceans(Flather,1976),SpallandRobinson(1989),etc.
• Morerecentlyaveryinteres5ngrevisit:Marchesielloetal.(2001)andBlayoandDebreu(2005)
• Interes5ngworkbyTemanandTribbia(2003)showingthatnon‐hydrosta5copenboundarycondi5onislessill‐posedthanhydrosta5ccase
TheMediterraneannestedmodelsLBCstrategy(Pinardietal.,2003)
• Fortracers,TandS,andbaroclinicveloci5es,collec5vely,use:
atouelowpoints(inflowcanbeprescribedfromcoarsemodel)• Forbarotropicvelocitynormalcomponents,
useinstead3differentforms:
• Whythesedifferentformsandwhatistherela5onshiptoFlather(1976)?
∂θ∂t
+ uNORMALCOARSE ∂θ
∂n= 0
UN =1
H +ηuNORMAL dz
−H
η
∫
UNF =
HC
HF
UNC ±
gHF
ηF ; UNF =
HC
HF
UNC ;
UNF =
HC
HF
UNC ±
gHF
(ηF −ηC )
θ
• Inaddi5on,allmodels,needtoconsiderthe‘INTERPOLATIONCONSTRAINT’,i.e.theconserva5onoftransportacrosstheopenboundaryalerinterpola5on
• Thisamountstohaveacorrec5onsdoneeachnes5ng5meonthefineresolu5onvelocitybarotropicfieldofthetype:
TheMediterraneannestedmodelsLBCstrategy(Pinardietal.,2003)
uC−HC
ηC
∫l1
l2
∫ dz dl = uINTERP−HF
ηF
∫l1
l2
∫ dz dl
UF =UINTERP −ΔTSF(x, y, z)
ThegeneralizedFlatherLBC(OddoandPinardi,OM,2008)
• Flather(1976):
• Wherethisformulacomesfrom?Flatherdoesnotexplainit.Ourderiva5onis:
• Imposinganequalitybetweentheconserva5onofmassinthecoarse(c)andfineresolu5on(F)domain:
UNF =UN
C −gH
ηC −ηF( )
∇ ⋅ u = 0
∂η∂t
+∇ ⋅ (H +η)U⎡⎣ ⎤⎦ = 0
∂ηC
∂t+∇ ⋅ (HC +ηC )
UC⎡⎣ ⎤⎦ =
∂ηF
∂t+∇ ⋅ (HF +ηF )
UF⎡⎣ ⎤⎦
ThegeneralizedFlatherLBC,cont.• Fromtheequalitybefore:
• Assumingthatthefreesurfacetendencycanbewri_enas:
• WeobtainthegeneralizedFlatherboundarycondi8on:
∂η∂t
+∇ ⋅ C η[ ] = 0
∂ηC
∂t+∇ ⋅ (HC +ηC )
UC⎡⎣ ⎤⎦ =
∂ηF
∂t+∇ ⋅ (HF +ηF )
UF⎡⎣ ⎤⎦
UNF =
HC +ηC
HF +ηF
UNC −
CN
HF +ηF
ηC −ηF( )
ThegeneralizedFlatherLBC,cont.
• ThegeneralizedFlatherboundarycondi8on:
• BecomestheFlather(1976)onlyif
• Thisisalsowhynes8ngandnestedmodelsbathymetryshouldnotbeverydifferentattheopenboundaryifFlather(1976)isused
UNF =
HC +ηC
HF +ηF
UNC −
CN
HF +ηF
ηC −ηF( )
HC ≈ HF = H ;
ηC ,F H ;
CN = gHUN
F =UNC −
gH
ηC −ηF( )
Scaleselec5veLBC• Knowingtheprinciples,nowwecanconsiderascale
separa5oninthefineresolu5onfield:supposeonepartspectrallyoverlapwiththecoarsefieldwhiletheotherisnew.Thus
• Alersomealgebratwonewequa5onsareformedforeachpor5onofthesolu5on:
ηF = ′ηF + ′′ηF
UF = ′U F + ′′U F
′UNF =
HC +ηC
HF + ′ηF
UNC − ′CN
HF + ′ηF
ηC − ′ηF( )
′′UNF = ′′ηF
HF +ηF
′′CN − ′UNF( )
Scaleselec5veversusnon‐scaleselec5vegeneralizedFlather:idealizedcase
Nestedmodeldomain
Timeofintegra5on
VelocitymagnitudeatpointS1
Referencesolu,on
Flather(1976)
Scaleselec5vegeneralizedFlather
Scaleselec5veversusnon‐scaleselec5vegeneralizedFlather:realis5ccase
Nestedmodel:From6‐7kmto2km
InsitudatatovalidatethemodelOutputwithDifferentLBC
Experiment
LBC
Exp1 Imposed
Exp2 Radia5on
Exp3 Scaleselec5ve
Scaleselec5veversusnon‐scaleselec5vegeneralizedFlather:realis5ccase
RP =rms(Exp2) or rms(Exp3)
rms(E xp1)Rela5vePerformanceIndex
RP =rms(Exp3)rms(E xp1)
Aprildata Junedata Octdata Decdata
RP =rms(Exp2)rms(E xp1)
TheCoastalRapidEnvironmentalAssessment(CREA)framework
• CREAistheevolu5onofMREAconcepts(Robinsonetal.,2000)forthecoastalarea
• Theaimistouseallinforma5ontoreduceuncertain5esinthe5‐7daysforecastofcurrents,temperatureandsalinitynearthecoastalareas
• CREAiscomposedof:– Basicopera5onaloceanographyanalysesandforecasts– Ahigherresolu5onnestedmodel– Observa5onsfromcoastalsystems– Ablendingalgorithm,mul5scaleop5malinterpola5onbyMarianoandBrown(1992)
– Ini5aliza5onstrategy(ThisisapartofSimoncelliPh.D.Thesis,2010)
TheCREAcomponents
(1) ThecoastalNetworks(ItalianandCroa5anEPAnetwork)
(2)Thenestedmodels,7,2kmand800meters
T (x, y, z,t) = TM (x, y, z,t) + TE (x, y, z,t) + ε
Twoinputdatasets:coarsemodeldataandlocalinsitudatawithdifferenterrorsMul5scalesubdivisionofthefield
Mul5‐inputandmul5scaleOI
(3)Theblendingalgorithm
TheBlendingimpact
a) 20’ 30’ 40’ 50’ 13oE
44oN
10’
20’
30’
40’
T[C°] 05!May!2003 IAFS
16.2
16.6
17
17.4
17.8
18.2
18.6
19
19.4
19.8
b) 20’ 30’ 40’ 50’ 13oE
44oN
10’
20’
30’
40’
T[C°] 05!May!2003 OBS
16.2
16.6
17
17.4
17.8
18.2
18.6
19
19.4
19.8
c) 20’ 30’ 40’ 50’ 13oE
44oN
10’
20’
30’
40’
T[C°] 05!May!2003 BA
16.2
16.6
17
17.4
17.8
18.2
18.6
19
19.4
19.8
d) 18’ 24’ 13oE
30.00’
36’ 42’
28’
32’
45oN 36.00’
40’
44’
T[C°] 05!May!2003 IAFS
15.3
15.5
15.7
15.9
16.1
16.3
16.5
16.7
16.9
17.1
17.3
17.5
17.7
17.9
18.1
18.3
18.5
18.7
e) 18’ 24’ 13oE
30.00’
36’ 42’
28’
32’
45oN 36.00’
40’
44’
T[C°] 05!May!2003 OBS
15.3
15.5
15.7
15.9
16.1
16.3
16.5
16.7
16.9
17.1
17.3
17.5
17.7
17.9
18.1
18.3
18.5
18.7
f) 18’ 24’ 13oE
30.00’
36’ 42’
28’
32’
45oN 36.00’
40’
44’
T[C°] 05!May!2003 BA
15.3
15.5
15.7
15.9
16.1
16.3
16.5
16.7
16.9
17.1
17.3
17.5
17.7
17.9
18.1
18.3
18.5
18.7
Fig. 8. SST fields on May 5th for the Emilia Romagna coastal area and the Gulf of Trieste.a) Emilia Romagna IAFS SST field; b) BA observed SST; c) BA blended initial conditionSST; d) Gulf of Trieste IAFS SST; e) BA observed SST; f) BA blended SST. (SST fieldshave been masked for mapping error greater than 30%)
56
COARSEMODEL INSITUDATA BLENDEDFIELD
AREA1
AREA2
20
16
17
18
19
18
15
TheCREAstrategy• Interpolatefromthecoarsegridtothefinerresolu5ongridand
extrapolateifneededusingclimatology• Blendthemodelinforma5onwiththeobserva5ons• Spin‐upthedynamicstohavehigherresolu5onscalesintheIC• ForcewithNWPanalysesandforecasts
CREA DAYIC DAY
(DE,D) IAFS
(BE,B) BA
(SU) IAFS BASPIN UP
Fig. 4. CREA initialization and forecast procedure.
52
Simoncellietal.,2010
ICday
BA‐BlendingIAFS‐Interpola5on
Theimprovementduetohighresolu5on(structured),observa5onsandspin‐up
a)
25 26 27 28 290
2
4
6
8
10
12
14
16
T[C°]d
ep
th [m
]35.7 36.2 36.7 37.2 37.70
2
4
6
8
10
12
14
16
S[psu]
CTD
AFS
D
B
SU
b)
20 22 24 26 280
5
10
15
20
25
T[C°]
de
pth
[m
]
35 35.5 36 36.5 37 37.5 380
5
10
15
20
25
S[psu]
c)
12 14 16 18 20 22 24 26 280
5
10
15
20
25
30
35
40
T[C°]
depth
[m
]
37 37.5 38 38.50
5
10
15
20
25
30
35
40
S[psu]
Fig. 13. Model results after one week of simulation from the Summer CREA experimentstarting August 11th. a) Emilia Romagna; b) Gulf of Trieste; c) Rovinj.
61
a)
25 26 27 28 290
2
4
6
8
10
12
14
16
T[C°]
depth
[m
]
35.7 36.2 36.7 37.2 37.70
2
4
6
8
10
12
14
16
S[psu]
CTD
AFS
D
B
SU
b)
20 22 24 26 280
5
10
15
20
25
T[C°]
de
pth
[m
]
35 35.5 36 36.5 37 37.5 380
5
10
15
20
25
S[psu]
c)
12 14 16 18 20 22 24 26 280
5
10
15
20
25
30
35
40
T[C°]
de
pth
[m
]
37 37.5 38 38.50
5
10
15
20
25
30
35
40
S[psu]
Fig. 13. Model results after one week of simulation from the Summer CREA experimentstarting August 11th. a) Emilia Romagna; b) Gulf of Trieste; c) Rovinj.
61
InterpolIC BlendedIC Spin‐upplusblending
%RMSEdecreasealeroneweekforecast
10% 20‐25% 30%
Conclusions• Opera5onaloceanographyisprovidingbasicanalysesformodelvalida5onanddevelopmentinmanypartsoftheworldocean
• Baroclinicmodelnes5ngforthecoastalareasworkingatallscales(openoceantoo,notshown)butneedfor:– Robustini5aliza5onmethods– Accurateorhighresolu5onatmosphericforcing– LateralBoundarycondi5ons:newgeneralizedFlatherpromising
• Possibletestbedforunstructuredgridvalida5on:CREAmethodsanddatabases.DatacouldbemadeavailabletothecommunityforNorthernAdria5cSea
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