2nd ENVISAT Summer School, ESA ESRIN, 16-26 August 2004Copyright 20©02, NERSC/ lhp
OVERVIEW OF OCEAN AND SEA ICE OVERVIEW OF OCEAN AND SEA ICE MODELLINGMODELLING
by
Johnny A. JohannessenNansen Environmental and Remote Sensing Center
Bergen, Norwayemail:[email protected]
2nd ENVISAT Summer School, ESA ESRIN, 16-26 August 2004Copyright 20©02, NERSC/ lhp
Lack of sufficient data collection and thereby general limitation regarding reliable descriptive analyses of the ocean inhibit satisfactory knowledge of the state and variable of the ocean.
In order to advance our understanding, provide forecasts and implement proper management system one need to find a compromise between observation requirements, actual data availability and mathematical model tools. This is also called optimal control problem (theory).
OCEAN AND SEA ICE MODELLING IS CAPITALIZING ON THIS
2nd ENVISAT Summer School, ESA ESRIN, 16-26 August 2004Copyright 20©02, NERSC/ lhp
CONTENT
- Introduction- Typical temporal and spatial scales- Classical models- European Data Assimilation Systems- Need for improvements- References
2nd ENVISAT Summer School, ESA ESRIN, 16-26 August 2004Copyright 20©02, NERSC/ lhp
Modeling of the marine environment are characterized by:
- dimensions in physical space (X - t);- number of state variables - hydrodynamic, chemical, bio-
geochemical;- vertical coordinate system- surface treatment (rigid lid, free surface) - parameterization of vertical and horizontal diffusion
(mixing in local models versus bulk models)- geographical coverage, time period, specific events or
processes;- grid type (rectilinear, curvilinear orthogonal, curvilinear non-
orthogonal);- numerical method; finite difference (use squares) or finite
element (use triangles)- numerical scheme and choice of time descritization; explicit,
implicit, semi-implicit- numerical consistent scheme and stable scheme.
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In physical space one can distinguish between local, regional and global models. Within each class the marine system can have distinct length-scales and time-scales. In fact length and time scales are somewhat coupled according to particular phenomenon (i.e. El Nino, tide, storm surges, etc). This constraints the choice of model resolution.
(after MERSEA IP)
The model accuracy (or reliability) depends on the resolution, precisions of the calculations, and quality of the data used to determine parameters and boundary conditions. Models also need accurate bathymetry at the adequate resolution in order to properly account for topographic steering.
The models are commonly forced by atmospheric fields including surface wind vector (wind stress and input of turbulent energy) and fluxes of heat (radiative, sensible and latent) directly taken from atmospheric models.
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Time scale Frequency (s-1)
Spectral windows(highlighted processes)
Smaller scale fluctations(filtered out processes)
1 s 1 Microscale processes3 D ”eddy ”turbulence(+ surface wav es)
Molecular diffusion
1 m10-2 Mesialscale processes
Internal wave sVertical microstructureInhibited “b liny”*turbulence
Eddy turbul ence
1 h10-4 Mesoscale processes
Inertial oscillations“Bliny turbu lence”
1 d10-5 Tides, storm surges
Diurnal va riations
Time-space characteristics
2nd ENVISAT Summer School, ESA ESRIN, 16-26 August 2004Copyright 20©02, NERSC/ lhp
Time scale Frequency (s-1)
Spectral windows(highlighted processes)
Smaller scale fluctations(filtered out processes)
1 w10 -6 Synop tisca le p roce sse s
Fron ta l cu rren tsMeande rs, ” ros sby”*turbul ence
Meso sca le var iab ilit y
1 mon th10 -7 Sea sona lsc a le proce sses “R ossby tu rbul ence”
1 yea r10 -8 Globa ls ca le proc esses
Clim atic pro ces sesSea sona l va riab ilit y
(Pal eo) clim aticsca leproces ses
Time-space characteristics
2nd ENVISAT Summer School, ESA ESRIN, 16-26 August 2004Copyright 20©02, NERSC/ lhp
Model dimensions in space and time- 1 D; simple model chosen to simulate vertical structure, mixed layer
dynamics including importance of turbulent mixing
- 2 D; depth integrated barotropic models (constant density in space/time are common for tides and storm surges modelling, and shallow water modelling
- 3 D; depth resolving baroclinic models for variable vertical density
Discretization of the continuity equation and equation of motion
?ρ/ ? t + . ρ u = 0 continuity equation
du/dt = − 1/ρ . p − 2Ω x u + g + F momentum equation
pressure Coriolis gravity other forces(friction, tides,..)
2nd ENVISAT Summer School, ESA ESRIN, 16-26 August 2004Copyright 20©02, NERSC/ lhp
Some fundamental hydrodynamic quantities
- Rossby radius of deformation;
Rd = (g h ∆ρ/ρ)1/2 / f
typical horizontal scale of the weather in the ocean; defines the length scale at which rotation effects (scaled by Coriolis parameter f) become as important as buoyancy effects.determined by ∆ρ/ρ
- Brunt-Vaisala frequency N; the measure of the stratification or vertical gradient in density (buoyancy)
N2 = g (- ρ δρ/δz)
2nd ENVISAT Summer School, ESA ESRIN, 16-26 August 2004Copyright 20©02, NERSC/ lhp
choice of vertical coordinate system
- z level; discretization in the vertical at fixed depth values - level models
- isopycnal; a fixed number of layers with constant density
- sigma; a bathymetry following coordinate system in shallow water
HYCOM: Hybrid coordinate ocean model (Bleck et al., 2002)-Combinesall 3 coordinate systems; z-level for mixed layer representation, isopycnic for the interior ocean density, sigma for shallow water terrain following coordinates.
LAYERMODELS
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OCEAN MODELLING
Models run at a global to basin scale are used to represent circulation of large oceanic water masses, whereas at a ‘nested’ regional or local scale with higher spatial resolution they provide finer detail, for example where eddy resolution is required. A nested model means that a high resolution regional model receives boundary conditions from an outer model with lower resolution. In this way one can insure proper representation of the general circulation into the regional area.
2nd ENVISAT Summer School, ESA ESRIN, 16-26 August 2004Copyright 20©02, NERSC/ lhp
OCEAN MODELLING
Ocean characteristics such as temperature, salinity and current velocity can be estimated in space and time by computer model simulation across a numerical ocean model grid. This means that one can get a fully 3-dimensional image of the ocean. Models can operate in hindcast mode to simulate historical time series of past conditions, and also in nowcast and forecast mode for operational applications.
2nd ENVISAT Summer School, ESA ESRIN, 16-26 August 2004Copyright 20©02, NERSC/ lhp
Grid Type
Satellite observations are usually slightly more favorable then in-situ point observations regarding representation in a grid cell.
Rectilinear orSpherical (RS)
Curvilinear Orthogonal (CO)
CurvilinearNon-orthogonal (NO)
2nd ENVISAT Summer School, ESA ESRIN, 16-26 August 2004Copyright 20©02, NERSC/ lhp
Example of Arakawa C-grid h: pressure, temperature, salinity, sea level
u: x-velocity
v: y-velocity
This is a so-called staggered grid with one grid-interval between variables h, u, v but where the latter two are shifted half a grid interval from h.
Ease the computations ofpressure gradient cont.to velocity field.
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Explicit scheme - only expressions at earlier time step n at right hand side
Implicit scheme - time step n+1 also at right hand side
Semi -implicit scheme - combines explicit and implicit schemes
2nd ENVISAT Summer School, ESA ESRIN, 16-26 August 2004Copyright 20©02, NERSC/ lhp
Authors Identifier VerticalGrid
HorizontalGrid
VerticalDiffusivity
HorizontalDiffusivity
Surface System
Blumburg-Mellor
POM σ - C CO/C TC or CVD Smag or CHD Free
Bryan-Cox-Semtner
BCS z - C RS/B RND/CA1 CHD rigid FOAM
Haidvogel SPEM σ - C/Spect
CO/C BML BiH rigid
R. Bleck etal.
MICOM Iso-pycnic
CO Bulk mixedlayer
CHD free
Oberhuber OBH ρ - C RS/B BML Smag free MICOMR. Bleck HYCOM hybrid KPP free TOPAZ
G. Madec OPA Z - C TKEclosure
rigid MERCATOR
SOME CLASSICAL OCEAN MODELS
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Four european ocean data assimilation system
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Zonal Section 26 ?N Salinity
MERCATOR
TOPAZ
FOAM
HYCOM
WOCE A05 JUL AUG 1992
WOCE A01 JAN FEB 1998
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Class2 Zonal Section 26°N Salinity
WOCEWOCE A01 JAN FEB 1998
IMPACT OF ASSIMILATION OF ARGO SALINITY PROFILE
FOAM (DEC20 2003)After assimilationof ARGO salinity profiles
assimilation of ARGO salinity profiles from DEC17 2003 on
FOAM (DEC15 2003)Before assimilationof ARGO salinity profiles
2nd ENVISAT Summer School, ESA ESRIN, 16-26 August 2004Copyright 20©02, NERSC/ lhp
Ice models characteristics
- define the ice concentration variable A as the fractional ice cover; i.e. 0 < A < 1;
- h is the local ice thickness and hI is the average thickness over the ice covered region;
- ice thickness distribution g(h);
- slab models - the vertical structure in the ice is neglected;
- ice rheology that parameterize internal ice stresses (plastic, elastic, viscos, pev, ev, pe);
- fluxes - melt rate on top, freeze rate at ice-ocean interface, freeze rate in open water, rate of frazil ice growth in
water column;
- snow-sea ice system - strong effect on albedo
2nd ENVISAT Summer School, ESA ESRIN, 16-26 August 2004Copyright 20©02, NERSC/ lhp
QuickTime™ og enGIF-dekomprimerer
kreves for å se dette bildet.
COURTECY KWOK
2nd ENVISAT Summer School, ESA ESRIN, 16-26 August 2004Copyright 20©02, NERSC/ lhp
Echam
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HadCm
2nd ENVISAT Summer School, ESA ESRIN, 16-26 August 2004Copyright 20©02, NERSC/ lhp
Need for improvement-Model resolution; enhanced resolution in the vertical and horizontal to obtain reliable simulations - global model at 10 km combined with nesting;
1/3° (PSY1) 1/15° (PSY2)
MERCATOR
SLA
2nd ENVISAT Summer School, ESA ESRIN, 16-26 August 2004Copyright 20©02, NERSC/ lhp
Need for improvement (cont.)-Model resolution; enhanced resolution in the vertical and horizontal to obtain reliable simulations - global model at 10 km combined with nesting;
1/3° (PSY1) 1/15° (PSY2)
MERCATOR
SST
2nd ENVISAT Summer School, ESA ESRIN, 16-26 August 2004Copyright 20©02, NERSC/ lhp
Need for improvement (cont.)-Model resolution; enhanced resolution in the vertical and horizontal to obtain reliable simulations - global model at 10 km combined with nesting;
1/3° (PSY1) 1/15° (PSY2)
MERCATOR
African Upwelling SST+VEL.
2nd ENVISAT Summer School, ESA ESRIN, 16-26 August 2004Copyright 20©02, NERSC/ lhp
Need for improvement (cont.)-Topography; Improved representation of topographic slopes is critical for simulations of mean and time-varying circulation;
SST+VEL
MICOM
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Need for improvement (cont.)
- Boundary layer representation; both surface mixed layers and benthic layers near the bottom need to be better simulated
- Coupling to ice models; ice models are essential for simulation of horizontal and vertical freshwater fluxes
- Mixing processes; mixing across isopycnals need better parameterization
- Surface fluxes; the ocean is driven primarily through a combination of buoyancy and momentum fluxes so reliable estimates of surface fluxes of heat, freshwater and momentum
2nd ENVISAT Summer School, ESA ESRIN, 16-26 August 2004Copyright 20©02, NERSC/ lhp
Need for improvement (cont.)- Advance and secure the observing system; integrated observations are needed to provide reliable description of the interior ocean state and to constrain (validate) models.
J1E2TPG2J1E2TP
J1E2J1
EKE (EKE (Pascual Pascual et al., 2004)et al., 2004)
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B lu m be r g, A .F . , and G. Me ll o r , 1987 : A De s cr ip ti on of a T h r ee - D im ens iona l Coa st a lOce a n C ir cu la ti on Mode l. I n : T hr e e- D ime ns i ona l C oas ta l Oce a n M ode ls , E d. Nor ma n S .Heap s , Coa st a l E s tu a r ine S c i . S e r ., Vo l . 4, AGU , Wa s h ing ton, D. C . , pp . 1 - 16.
B r yan , K . , 1969 : A nu m e r ic a l m e thod fo r th e s tudy o f t he c i r c ul at ion o f the wor ld ocean .J . C o m p. P hys. , 4 , 347 - 376 .
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Cox , M .D . , 1984 : A p r imiti ve equa ti on th r ee - d im ens i ona l m ode l o f th e oce a n. Te c h. Rep .1 , Oce a n G r oup, NOAA Geophy s . F lu id Dyn. L a b. , Un ive r s it y of P r inc e ton , N ew J e r sey ,250 pp.
Dav ie s , A. M . , 1987 : S pec tr a l M ode ls i n Con ti nen ta l S he l f S ea Oceanog r aphy . I n : T hr e e-D im en s ion al Co a s ta l O cean Mode ls , Ed . No rm an S . H e aps , C oas ta l E st ua r in e S c i. S e r . ,Vo l. 4 , AGU , W ash ing ton, D . C. , 71 - 106 pp.
Ha i dvoge l, D .B ., A. Be c km a n, and K .S . Hed s t r ö m , 1992 : Dyn am ic a l si mu la t ion s o ffi lam en t f or m a ti on and e vo lut ion i n the coa st a l tr ans iti on z one. J . G e ophys . R e s . , 96( C 8) ,15 ,017-15 ,040.
Ho ll and , W . R . , and L .B . L in , 1975a : On the O ri gin o f M eso s ca le Edd ie s and t he irCon tri bu ti on to th e Gen e ra l C ir cu la ti on o f t he Oce a n, I , A P r e l imi na r y N um e r ic a lE xper im en t. J . P hys. Oce a nogr . , 5, 642-657 .
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RECOMMENDED LITTERATURE
2nd ENVISAT Summer School, ESA ESRIN, 16-26 August 2004Copyright 20©02, NERSC/ lhp
O'B ri en , J . J . , 1975 : Mod el s of coa st a l upwe lli ng - A rev iew . Nu m e ri ca l Mode ls o f O ceanC ir cu la ti on, Acad em y o f S c ienc e s , Wa s hing ton, D. C ., pp . 204 - 215. O'B ri en , J .J . (E d. ) ,1986 : A dvanced Phy si ca l Oceanog r aph ic Nu m er ic al M ode ll ing . N ATO A S I S e rie s , S er .C : Ma the ma tic a l and P hys ica l S cience s, Vo l . 186,
Rob in s on, A. R ., 1986 : Da ta A ss imil a ti on , M e so s ca le Dyna mi cs and D yna mi ca lF or e cas ti ng . I n : Adv a nced Phy si ca l O ceanog r aph ic Nu m er ic al M ode lling , E d. J a m e s J .O'B ri en , Pr oceed ing s o f the NA T O Advan c ed St udy In st it ut e , B anyu ls -su r- Me r, F r a nce ,Jun e 2 -15, 1985, NA T O A SI S e r . C , Vo l. 186 , D. Re ide l P ub l . Co. , pp . 465 -483 .
S a rm ie n to, J. L. , and K . B ry a n, 1982: An ocean t r anpo rt m ode l fo r t he No rt h A tl an ti c . J.Geophy s . Re s ., 87 , 394 - 408.
S e mt ne r , 1986 : H is to r y and m e thodo logy of m ode ll ing the ci rcu la tion o f the wor ld ocean .I n : Advan c ed P hys ic al Oc e anogr a ph ic Nu m e ri ca l Mode lli ng , E d. J. J. O' B ri en , NA T OA SI Se ri es C , 186 ,
S e mt ne r , A. J ., and R .M . C herv in , 1992 : Ocean gene ra l ci rcu lati on fr o m a g loba l eddy-r eso lv ing mod el . J. Geophy s . Re s ., 97 ( C4 ), 5493 - 5550.
Sm o lark ie w icz, P .K ., 1983 : A sim p le pos iti ve d e fin it e advec ti on sche m e w it h sm a llim p li cit d if fu si on. Mon . We at her Rev ., 111, 479 -486.
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