Recent Developments in Recent Developments in Ocean ModelingOcean Modeling

Edmo CamposEdmo CamposOcean Numerical Modeling Laboratory Ocean Numerical Modeling Laboratory

LABMONLABMON

Oceanographic Institute – Univ. Sao PauloOceanographic Institute – Univ. Sao Paulo

Credits to E. Chassignet, COAPS/FSU, and S. Griffies, GFDL,

Some common uses of ocean Some common uses of ocean modelsmodels

• Scientifically rationalize the observed ocean. Scientifically rationalize the observed ocean. – To test hypotheses for physical, chemical, or biological To test hypotheses for physical, chemical, or biological

mechanisms underlying observations.mechanisms underlying observations.

• Predict future changes in the ocean.Predict future changes in the ocean. – To forecast mesoscale features (e.g., Brazil/Malvinas To forecast mesoscale features (e.g., Brazil/Malvinas

confluence, Gulf Stream)confluence, Gulf Stream)– To determine scenarios for large scale trends arising from To determine scenarios for large scale trends arising from

changes in anthropogenic forcing (e.g., changes/collapse in changes in anthropogenic forcing (e.g., changes/collapse in Atlantic meridional circulation in a warmer world).Atlantic meridional circulation in a warmer world).

• Provide scientifically based advice to policy Provide scientifically based advice to policy makers for managing coastal related commercemakers for managing coastal related commerce– fisheries and other resources, shipping and recreation, fisheries and other resources, shipping and recreation,

energy use policy, waste disposal , coastal development, energy use policy, waste disposal , coastal development, coastal impacts of climate change, etc.coastal impacts of climate change, etc.

Coastal and climate interactionsCoastal and climate interactions

Coastal influencesLarge-scale coupled climate dynamics

Schematic from Hans Von Storch

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Ocean Circulation is regarded today as a key component of the climate system.

What about weather and seasonal climate forecasting?

Ocean models and the Climate Ocean models and the Climate SystemSystem

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Algal blooms and fish population variability

Climate-sensitive vector borne diseases, eg. Malaria and dengue fever.

Waterborne diseases affected by rainfall, e.g. leptospirosis and cholera.

floods

Nutrient input, vertical stratification, SST variability

Wind variations

crops

Precipitation variability Variations in Plata/Patos low

salinity water

Understanding the coastal land-ocean-atmosphere interactions is crucial in the understanding of extreme events at seasonal and intra-seasonal scales

Coastal influences

The CatarinaThe Catarina

Pezza and Simmonds (2005)

Trajectory and maximum SST during the whole Trajectory and maximum SST during the whole period period (SST slightly below average but note 26.5C near (SST slightly below average but note 26.5C near where the trajectory started)where the trajectory started)

The CatarinaThe Catarina

Some Challenges for Ocean Some Challenges for Ocean ModelingModeling

• Role of mesoscale eddiesRole of mesoscale eddies

• Influence of marginal Influence of marginal seas and topographic seas and topographic control on the open control on the open oceanocean

• Influence of open ocean Influence of open ocean circulation on shelf circulation on shelf circulation and circulation and ecosystemsecosystems

• Coupling ocean-ice-wave-Coupling ocean-ice-wave-atmosphereatmosphere

• Improved understanding Improved understanding of modes of large-scale of modes of large-scale ocean variabilityocean variability

• Interactions between the Interactions between the mixed layer, atmosphere mixed layer, atmosphere and subsurface oceanand subsurface ocean

• Estimation of ocean Estimation of ocean state, ocean initialization state, ocean initialization

• Physically consistent Physically consistent estimates and estimates and parameterizations of parameterizations of diapycnal mixingdiapycnal mixing

• Replacing numerical Replacing numerical closures with physical closures with physical parameterizationsparameterizations

• Reducing bias induced Reducing bias induced by model numericsby model numerics

Ocean model considerations (1)Ocean model considerations (1)• Nearly every question about ocean modeling boils Nearly every question about ocean modeling boils

down to three issuesdown to three issues– Fundamentals Fundamentals – Boundary forcing Boundary forcing – Analysis methodsAnalysis methods

• Fundamentals are concerned with underlying physical, Fundamentals are concerned with underlying physical, mathematical, and numerical aspects of an ocean mathematical, and numerical aspects of an ocean model.model. – Geophysical and computational fluid mechanics Geophysical and computational fluid mechanics – Oceanography—descriptive and theoreticalOceanography—descriptive and theoretical– Statistical physics—for subgrid scale parameterizationsStatistical physics—for subgrid scale parameterizations– Algorithm design—methods to solve the equations on a Algorithm design—methods to solve the equations on a

computercomputer

• Equations:Equations: – Hydrostatic or non-hydrostatic? Hydrostatic or non-hydrostatic? – Boussinesq or non-Boussinesq? Boussinesq or non-Boussinesq? – Rigid lid or free surface? Rigid lid or free surface? – Virtual tracer fluxes or real water fluxes? Virtual tracer fluxes or real water fluxes? – Advective form of momentum equations or vector invariant Advective form of momentum equations or vector invariant

form?form?

Ocean Model Considerations (2)Ocean Model Considerations (2)• Formulation:Formulation:

– Vertical coordinates—geopotential, pressure, terrain, Vertical coordinates—geopotential, pressure, terrain, isopycnal, generalized hybrid? isopycnal, generalized hybrid?

– Horizontal grid: Arakawa A,Horizontal grid: Arakawa A,B,C,B,C,D,E, spectral, finite D,E, spectral, finite element? element?

– Horizontal grid structure: regular spherical coordinates, Horizontal grid structure: regular spherical coordinates, regular generalized, tripolar, cubed sphere, icosahedra, regular generalized, tripolar, cubed sphere, icosahedra, nested, unstructured finite elements, time dependent nested, unstructured finite elements, time dependent adaptive? adaptive?

– Finite volume foundation? Finite volume foundation? • Algorithms:Algorithms:

– Time steppingTime stepping– Discrete advection operatorsDiscrete advection operators– Coriolis forceCoriolis force– Implicit vertical physical processesImplicit vertical physical processes– Pressure gradient forcePressure gradient force– Equation of stateEquation of state

• Subgrid scale closure: Subgrid scale closure: Unresolved processes, both Unresolved processes, both physical and numerical, are ubiquitous and often physical and numerical, are ubiquitous and often of first order importance.of first order importance.

• The choice of the vertical coordinate The choice of the vertical coordinate system issystem is the single most important aspect the single most important aspect of an ocean model's designof an ocean model's design and and introduces the largest source of truncation introduces the largest source of truncation error (for a given horizontal resolution)error (for a given horizontal resolution)

• Rotating and stratified fluidsRotating and stratified fluids =>=> dominance dominance of lateral over vertical transportof lateral over vertical transport

• Hence, it is traditional in ocean modeling to Hence, it is traditional in ocean modeling to orient the two horizontal coordinates orient the two horizontal coordinates orthogonal to the local vertical direction as orthogonal to the local vertical direction as determined by gravitydetermined by gravity

• The practical issues of representation and The practical issues of representation and subgrid scale parameterization are often subgrid scale parameterization are often directly linked to the vertical coordinate directly linked to the vertical coordinate choicechoice (Griffies et al., 2000).(Griffies et al., 2000).

Considerations in Choosing a Considerations in Choosing a Vertical CoordinateVertical Coordinate

1.1. The vertical coordinate must be monotonic The vertical coordinate must be monotonic with depth for any stably stratified density with depth for any stably stratified density profileprofile

2.2. Changes in density due to numerics should be Changes in density due to numerics should be much smaller than changes due to physical much smaller than changes due to physical processesprocesses

3.3. Coordinate surfaces should coincide with Coordinate surfaces should coincide with locally-referenced neutral surfaces to permit a locally-referenced neutral surfaces to permit a nearly two-dimensional representation of nearly two-dimensional representation of advection and isoneutral mixing.advection and isoneutral mixing.

4.4. Thermobaric effects (i.e., compressibility Thermobaric effects (i.e., compressibility dependence on T and S) should be included in dependence on T and S) should be included in the pressure gradient termthe pressure gradient term

Currently, there areCurrently, there are three main vertical three main vertical coordinates coordinates in use, none of which provides in use, none of which provides

universal utility. universal utility.

““Development in Ocean Climate Modeling”Development in Ocean Climate Modeling” by Griffies, Boening, Bryan, by Griffies, Boening, Bryan, Chassignet, Gerdes, Hasumi, Hirst, Treguier, and Webb (2000, Ocean Chassignet, Gerdes, Hasumi, Hirst, Treguier, and Webb (2000, Ocean

Modelling)Modelling)

Key advantages of Key advantages of zz-models-models

•The simplest numerical discretization: The simplest numerical discretization: this has allowed this has allowed zz-models to be used -models to be used widely soon after their initial widely soon after their initial developmentdevelopment

•The equation of state for ocean water The equation of state for ocean water and the pressure gradient can be and the pressure gradient can be accurately represented accurately represented

•The surface mixed layer is naturally The surface mixed layer is naturally parameterized using parameterized using zz-coordinates-coordinates

Disadvantages of Disadvantages of zz-models-models

•The representation of tracer advection The representation of tracer advection and diffusion along inclined density or and diffusion along inclined density or neutral surfaces in the ocean interior neutral surfaces in the ocean interior is difficult (spurious numerically is difficult (spurious numerically induced diapycnal mixing that can be induced diapycnal mixing that can be much larger than the observed much larger than the observed background values; see Griffies background values; see Griffies et alet al., ., 1998, for details)1998, for details)

•Representation of bottom topography Representation of bottom topography and parameterization of the bottom and parameterization of the bottom boundary layer is unnaturalboundary layer is unnatural

Key advantages of Key advantages of sigmasigma- (or - (or terrain following) modelsterrain following) models

•Smooth representation of the ocean Smooth representation of the ocean bottom topography, with coordinate bottom topography, with coordinate isolines concentrated in regions where isolines concentrated in regions where bottom boundary layer processes are bottom boundary layer processes are most importantmost important

•Natural framework to parameterize Natural framework to parameterize bottom boundary layer processes.bottom boundary layer processes.

Disadvantages of Disadvantages of sigmasigma--modelsmodels

•The surface mixed layer is not as well The surface mixed layer is not as well represented as with the represented as with the zz-coordinate. -coordinate. The vertical distance between grid The vertical distance between grid points generally increases upon moving points generally increases upon moving away from the continental shelf regions away from the continental shelf regions less vertical resolution less vertical resolution

•The horizontal pressure force consists The horizontal pressure force consists of two sizable terms, each having of two sizable terms, each having separate numerical errors which separate numerical errors which generally do not cancel generally do not cancel spurious spurious pressure forces that drive nontrivial pressure forces that drive nontrivial unphysical currentsunphysical currents

Key advantages of Key advantages of isopycnicisopycnic modelsmodels

•Tracer transport in the ocean interior Tracer transport in the ocean interior occurs along directions defined by occurs along directions defined by locally referenced potential density locally referenced potential density (i.e., neutral directions) (i.e., neutral directions) no spurious no spurious numerical mixing as long as isopycnals numerical mixing as long as isopycnals are parallel to neutral directionsare parallel to neutral directions

•The bottom topography is represented The bottom topography is represented in a piecewise linear fashion, hence in a piecewise linear fashion, hence avoiding the need to distinguish bottom avoiding the need to distinguish bottom from side as done with from side as done with zz-models-models

Disadvantages of Disadvantages of isopycnicisopycnic modelsmodels

•A density-coordinate is an A density-coordinate is an inappropriate framework for inappropriate framework for representing the surface mixed layer or representing the surface mixed layer or bottom boundary layer, since these bottom boundary layer, since these boundary layers are mostly unstratifiedboundary layers are mostly unstratified

• Inclusion of thermobaricity in order to Inclusion of thermobaricity in order to represent the effects of a realistic represent the effects of a realistic (nonlinear) equation of state is non-(nonlinear) equation of state is non-trivialtrivial

Ideally, an ocean general circulation Ideally, an ocean general circulation model (OGCM) shouldmodel (OGCM) should

• retain its water mass characteristics for centuriesretain its water mass characteristics for centuries (a characteristic of (a characteristic of isopycnicisopycnic coordinates), coordinates),

(b) have high vertical resolution in the surface mixed (b) have high vertical resolution in the surface mixed layer (a characteristic of layer (a characteristic of zz-level coordinates) for a -level coordinates) for a proper representation of thermodynamical and proper representation of thermodynamical and biochemical processes,biochemical processes,

(c) maintain sufficient vertical resolution in unstratified(c) maintain sufficient vertical resolution in unstratified or weakly-stratified regions of the ocean, or weakly-stratified regions of the ocean,

(d) have high vertical resolution in coastal regions (d) have high vertical resolution in coastal regions (a characteristic of (a characteristic of terrain-followingterrain-following coordinates). coordinates).

Hybrid Coordinates

MICOM

HYCOM

The prototype HYCOM “re-The prototype HYCOM “re-gridder” or “grid generator” gridder” or “grid generator” (Bleck, 2002)(Bleck, 2002) Design Principles (ALE):Design Principles (ALE):• T/S conservativeT/S conservative• Monotonicity-preserving (no new T/S Monotonicity-preserving (no new T/S

extrema during re-gridding)extrema during re-gridding)• Layer too dense => entrain lighter water Layer too dense => entrain lighter water

from abovefrom above• Layer too light => entrain denser water Layer too light => entrain denser water

from belowfrom below• Maintain finite layer thickness in upper Maintain finite layer thickness in upper

ocean but allow massless layers on sea ocean but allow massless layers on sea floorfloor

• Minimize seasonal vertical migration of Minimize seasonal vertical migration of coordinate layers by keeping coordinate layers by keeping non-non-isopycnicisopycnic layers near top of water column. layers near top of water column.

The hybrid coordinate is one that is The hybrid coordinate is one that is isopycnalisopycnal in in the open, stratified ocean, but smoothly reverts to the open, stratified ocean, but smoothly reverts to a a terrain-following terrain-following coordinate in shallow coastal coordinate in shallow coastal regions, and to regions, and to pressurepressure coordinate in the mixed coordinate in the mixed layer and/or unstratified seas.layer and/or unstratified seas.

FFlloor r iiddaa

Cuba Cuba

zz σσ-z-z

σσ HybridHybrid

2007 LOM Workshop2007 LOM Workshop Bergen, Norway - Aug. 2007Bergen, Norway - Aug. 2007 2828

Different nested domains off Brazilian coast

• up to 1/32 degree horizontal res. 22 layers

• Initial and boundary conditions taken from coarse resolution run.

•Funded by PETROBRAS

REMO: A Brazilian Network for Ocean Modeling and REMO: A Brazilian Network for Ocean Modeling and ObservationsObservations

A hierarchy of Numerical Models, including HYCOM, is being used for developing an Ocean Prediction system in Brazil.

2007 LOM Workshop2007 LOM Workshop Bergen, Norway - Aug. 2007Bergen, Norway - Aug. 2007 2929

For the Near Future

Example for global: Hide coordinate poles over land

Honrizontal Grid Structure Choices

CUBE SPHERE

Icosahedral or geodesic grids (Buckminister Fuller)No singularities and close to isotropic over sphere.

Time dependent adaptive grids. Add resolution to regions as needed (ICOM, D. Marshall)

Re=8000

Re=8000

Initially approx. Initially approx. 1/4 degree 1/4 degree

everywhere - everywhere - here approx. 1 – here approx. 1 –

1/30 1/30 °°

Elements ≈ Elements ≈ 65,00065,000

ICOMICOM

Second GenerationSecond Generation

• Horizontal resolution: 0.3-1.0 km in the Horizontal resolution: 0.3-1.0 km in the coastal region;coastal region;

• Generalized terrain-following coordinates: Generalized terrain-following coordinates: 46 layers: 10 uniform layers in the surface 46 layers: 10 uniform layers in the surface and bottom boundary layers, respectively.and bottom boundary layers, respectively.

• 1500 m cutoff off Georges Bank1500 m cutoff off Georges Bank• Capable to nest to the coasta-estuarine Capable to nest to the coasta-estuarine

model with a horizontal resolution of ~10 -model with a horizontal resolution of ~10 -500 m;500 m;

Third GenerationThird Generation

• Horizontal resolution: 0.5-1.0 km in Horizontal resolution: 0.5-1.0 km in the coastal region;the coastal region;

• Sigma-coordinates: 31 vertical layersSigma-coordinates: 31 vertical layers• 300 m cutoff off Georges Bank 300 m cutoff off Georges Bank

FVCOM UNSTRUCRURED GRID (Chen, UMASSD)

Gulf of Maine

Second Generation Second Generation Third Generation Third Generation

Surface sigma level: does not resolve Surface sigma level: does not resolve the near-surface current because the the near-surface current because the horizontal velocity is calculated at the horizontal velocity is calculated at the mid-point of the first sigma layer, which mid-point of the first sigma layer, which changes with depth. changes with depth.

At the 2-m below the surface: Resolve At the 2-m below the surface: Resolve the near-surface current better with the the near-surface current better with the thin uniform layers at the surface.. thin uniform layers at the surface..

Closing commentsClosing comments• Models continue to evolve, with new ideas Models continue to evolve, with new ideas

presently being developedpresently being developed– Generalized vertical coordinatesGeneralized vertical coordinates– Novel horizontal grids Novel horizontal grids – Numerical methods (time stepping, advection Numerical methods (time stepping, advection

operators, etc)operators, etc)– Subgrid scale parameterizationsSubgrid scale parameterizations

• Carefully choose your model (both code as Carefully choose your model (both code as well as resolution and parameterization) to well as resolution and parameterization) to have an a priori notion of what “ocean” will have an a priori notion of what “ocean” will be simulatedbe simulated