overview of ocean and sea ice modelling · inhibited “bliny”* turbulence eddy turbul ence 1 h...

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]


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


CONTENT

- Introduction- Typical temporal and spatial scales- Classical models- European Data Assimilation Systems- Need for improvements- References


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.


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.


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


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


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,..)


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)


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


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.


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.


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)


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.


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


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


Four european ocean data assimilation system


Zonal Section 26 ?N Salinity

MERCATOR

TOPAZ

FOAM

HYCOM

WOCE A05 JUL AUG 1992

WOCE A01 JAN FEB 1998


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


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


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COURTECY KWOK


Echam


HadCm


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


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


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.


Need for improvement (cont.)-Topography; Improved representation of topographic slopes is critical for simulations of mean and time-varying circulation;

SST+VEL

MICOM


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


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)


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 .

Coop e r, C .K . , and J .D . T ho m pson , 1989a : Hu r r ic a ne gen e ra te d cu rr en ts on t he ou t ercon ti nen ta l she lf , 1, Mode l f or m u la ti on a nd ve rif ic a ti on. J . Geophy s . Re s ., 94, 12,513 -12539 .

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 .

Hu rl bur t, H . E . , and J. D . Tho m pson , 1980 : A nu me r ic a l s tudy of Loop Cu rr en t in tr us i onand eddy s hedd ing. J . P hy s . Oceanog r ., 10, 1611 - 1651.

RECOMMENDED LITTERATURE


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.

overview of ocean and sea ice modelling · inhibited “bliny”* turbulence eddy turbul ence 1 h...

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