1. Recent Developments in Ocean Modeling Edmo Campos Ocean Numerical Modeling Laboratory LABMON Oceanographic Institute – Univ. Sao Paulo Credits to E. Chassignet, COAPS/FSU, and S. Griffies, GFDL,

2. Some common uses of ocean models Scientifically rationalize the observed ocean. Scientifically rationalize the observed ocean. –To test hypotheses for physical, chemical, or biological mechanisms underlying observations. Predict future changes in the ocean. Predict future changes in the ocean. –To forecast mesoscale features (e.g., Brazil/Malvinas confluence, Gulf Stream)‏ –To determine scenarios for large scale trends arising from changes in anthropogenic forcing (e.g., changes/collapse in Atlantic meridional circulation in a warmer world). Provide scientifically based advice to policy makers for managing coastal related commerce Provide scientifically based advice to policy makers for managing coastal related commerce –fisheries and other resources, shipping and recreation, energy use policy, waste disposal, coastal development, coastal impacts of climate change, etc.

3. Coastal and climate interactions Coastal influences Large-scale coupled climate dynamics Schematic from Hans Von Storch

4. 4 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 System

5. 5 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

6. The Catarina

7. Pezza and Simmonds (2005)‏ Trajectory and maximum SST during the whole period (SST slightly below average but note 26.5C near where the trajectory started) ‏ The Catarina

8. Some Challenges for Ocean Modeling Role of mesoscale eddies Role of mesoscale eddies Influence of marginal seas and topographic control on the open ocean Influence of marginal seas and topographic control on the open ocean Influence of open ocean circulation on shelf circulation and ecosystems Influence of open ocean circulation on shelf circulation and ecosystems Coupling ocean-ice-wave- atmosphere Coupling ocean-ice-wave- atmosphere Improved understanding of modes of large-scale ocean variability Improved understanding of modes of large-scale ocean variability Interactions between the mixed layer, atmosphere and subsurface ocean Interactions between the mixed layer, atmosphere and subsurface ocean Estimation of ocean state, ocean initialization Estimation of ocean state, ocean initialization Physically consistent estimates and parameterizations of diapycnal mixing Physically consistent estimates and parameterizations of diapycnal mixing Replacing numerical closures with physical parameterizations Replacing numerical closures with physical parameterizations Reducing bias induced by model numerics Reducing bias induced by model numerics

9. Ocean model considerations (1)‏ Nearly every question about ocean modeling boils down to three issues Nearly every question about ocean modeling boils down to three issues –Fundamentals –Boundary forcing –Analysis methods Fundamentals are concerned with underlying physical, mathematical, and numerical aspects of an ocean model. Fundamentals are concerned with underlying physical, mathematical, and numerical aspects of an ocean model. –Geophysical and computational fluid mechanics –Oceanography—descriptive and theoretical –Statistical physics—for subgrid scale parameterizations –Algorithm design—methods to solve the equations on a computer Equations: Equations: –Hydrostatic or non-hydrostatic? –Boussinesq or non-Boussinesq? –Rigid lid or free surface? –Virtual tracer fluxes or real water fluxes? –Advective form of momentum equations or vector invariant form?

10. Ocean Model Considerations (2)‏ Formulation: Formulation: –Vertical coordinates—geopotential, pressure, terrain, isopycnal, generalized hybrid? –Horizontal grid: Arakawa A,B,C,D,E, spectral, finite element? –Horizontal grid structure: regular spherical coordinates, regular generalized, tripolar, cubed sphere, icosahedra, nested, unstructured finite elements, time dependent adaptive? –Finite volume foundation? Algorithms: Algorithms: –Time stepping –Discrete advection operators –Coriolis force –Implicit vertical physical processes –Pressure gradient force –Equation of state Subgrid scale closure: Unresolved processes, both physical and numerical, are ubiquitous and often of first order importance. Subgrid scale closure: Unresolved processes, both physical and numerical, are ubiquitous and often of first order importance.

11. The choice of the vertical coordinate system is the single most important aspect of an ocean model's design and introduces the largest source of truncation error (for a given horizontal resolution)‏ The choice of the vertical coordinate system is the single most important aspect of an ocean model's design and introduces the largest source of truncation error (for a given horizontal resolution)‏ Rotating and stratified fluids => dominance of lateral over vertical transport Rotating and stratified fluids => dominance of lateral over vertical transport Hence, it is traditional in ocean modeling to orient the two horizontal coordinates orthogonal to the local vertical direction as determined by gravity Hence, it is traditional in ocean modeling to orient the two horizontal coordinates orthogonal to the local vertical direction as determined by gravity The practical issues of representation and subgrid scale parameterization are often directly linked to the vertical coordinate choice (Griffies et al., 2000). The practical issues of representation and subgrid scale parameterization are often directly linked to the vertical coordinate choice (Griffies et al., 2000).

12. Considerations in Choosing a Vertical Coordinate 1. The vertical coordinate must be monotonic with depth for any stably stratified density profile 2. Changes in density due to numerics should be much smaller than changes due to physical processes 3. Coordinate surfaces should coincide with locally- referenced neutral surfaces to permit a nearly two- dimensional representation of advection and isoneutral mixing. 4. Thermobaric effects (i.e., compressibility dependence on T and S) should be included in the pressure gradient term

13. Currently, there are three main vertical coordinates in use, none of which provides universal utility. “Development in Ocean Climate Modeling” by Griffies, Boening, Bryan, Chassignet, Gerdes, Hasumi, Hirst, Treguier, and Webb (2000, Ocean Modelling)‏

14. Key advantages of z-models Key advantages of z-models The simplest numerical discretization: this has allowed z-models to be used widely soon after their initial development The simplest numerical discretization: this has allowed z-models to be used widely soon after their initial development The equation of state for ocean water and the pressure gradient can be accurately represented The equation of state for ocean water and the pressure gradient can be accurately represented The surface mixed layer is naturally parameterized using z-coordinates The surface mixed layer is naturally parameterized using z-coordinates

15. Disadvantages of z-models The representation of tracer advection and diffusion along inclined density or neutral surfaces in the ocean interior is difficult (spurious numerically induced diapycnal mixing that can be much larger than the observed background values; see Griffies et al., 1998, for details)‏ The representation of tracer advection and diffusion along inclined density or neutral surfaces in the ocean interior is difficult (spurious numerically induced diapycnal mixing that can be much larger than the observed background values; see Griffies et al., 1998, for details)‏ Representation of bottom topography and parameterization of the bottom boundary layer is unnatural Representation of bottom topography and parameterization of the bottom boundary layer is unnatural

16. Key advantages of sigma- (or terrain following) models Smooth representation of the ocean bottom topography, with coordinate isolines concentrated in regions where bottom boundary layer processes are most important Smooth representation of the ocean bottom topography, with coordinate isolines concentrated in regions where bottom boundary layer processes are most important Natural framework to parameterize bottom boundary layer processes. Natural framework to parameterize bottom boundary layer processes.

17. Disadvantages of sigma-models The surface mixed layer is not as well represented as with the z-coordinate. The vertical distance between grid points generally increases upon moving away from the continental shelf regions  less vertical resolution The surface mixed layer is not as well represented as with the z-coordinate. The vertical distance between grid points generally increases upon moving away from the continental shelf regions  less vertical resolution The horizontal pressure force consists of two sizable terms, each having separate numerical errors which generally do not cancel  spurious pressure forces that drive nontrivial unphysical currents The horizontal pressure force consists of two sizable terms, each having separate numerical errors which generally do not cancel  spurious pressure forces that drive nontrivial unphysical currents

18. Key advantages of isopycnic models Tracer transport in the ocean interior occurs along directions defined by locally referenced potential density (i.e., neutral directions)  no spurious numerical mixing as long as isopycnals are parallel to neutral directions Tracer transport in the ocean interior occurs along directions defined by locally referenced potential density (i.e., neutral directions)  no spurious numerical mixing as long as isopycnals are parallel to neutral directions The bottom topography is represented in a piecewise linear fashion, hence avoiding the need to distinguish bottom from side as done with z-models The bottom topography is represented in a piecewise linear fashion, hence avoiding the need to distinguish bottom from side as done with z-models

19. Disadvantages of isopycnic models A density-coordinate is an inappropriate framework for representing the surface mixed layer or bottom boundary layer, since these boundary layers are mostly unstratified A density-coordinate is an inappropriate framework for representing the surface mixed layer or bottom boundary layer, since these boundary layers are mostly unstratified Inclusion of thermobaricity in order to represent the effects of a realistic (nonlinear) equation of state is non-trivial Inclusion of thermobaricity in order to represent the effects of a realistic (nonlinear) equation of state is non-trivial

20. Spurious mixing: Challenge for ALL models Mixing in thermocline VERY small: O(10 -5 m 2 /sec) according to tracer measurements, both in both equatorial and mid-latitude regions. Can ocean models maintain this, or smaller, with their numerics? Isopycnal models by definition are fine when run in adiabatic mode. But what about more realistic situations with nonlinear equation of state, mixed layers merging with adiabatic interior (matching problems), etc. Z and Sigma models have no trivial limit where all is fine. They must always depend on numerical integrity of transport operators. Problem becomes MORE difficult at refined resolutions

21. Possible solutions Hybrid models with isopycnal interior. Hope they handle the nonlinear equation of state and matching between vertical coordinate regions in a quasi-adiabatic manner. Hybrid models with isopycnal interior. Hope they handle the nonlinear equation of state and matching between vertical coordinate regions in a quasi-adiabatic manner. Sophisticated numerical advection operators (not yet available)‏ Sophisticated numerical advection operators (not yet available)‏ Dissipate via quasi-adiabatic operators such as Gent- McWilliams skewsion or variants. This has worked in idealized tests, though research continues. Maybe of use for non-isopycnal models in combination with sophisticated advection operators. Dissipate via quasi-adiabatic operators such as Gent- McWilliams skewsion or variants. This has worked in idealized tests, though research continues. Maybe of use for non-isopycnal models in combination with sophisticated advection operators. Is this an issue for operational modeling? Perhaps it is, but certainly is critical for climate simulations, especially in presence of mesoscale eddies. Is this an issue for operational modeling? Perhaps it is, but certainly is critical for climate simulations, especially in presence of mesoscale eddies.

22. Ideally, an ocean general circulation model (OGCM) should retain its water mass characteristics for centuries retain its water mass characteristics for centuries (a characteristic of isopycnic coordinates), (a characteristic of isopycnic coordinates), (b) have high vertical resolution in the surface mixed layer (a characteristic of z-level coordinates) for a proper representation of thermodynamical and biochemical processes, (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 (a characteristic of terrain-following coordinates). (a characteristic of terrain-following coordinates).

23. Hybrid Coordinates

24. MICOM HYCOM

25. The prototype HYCOM “re-gridder” or “grid generator” (Bleck, 2002)‏ Design Principles (ALE): Design Principles (ALE): T/S conservative T/S conservative Monotonicity-preserving (no new T/S extrema during re-gridding)‏ Monotonicity-preserving (no new T/S extrema during re-gridding)‏ Layer too dense => entrain lighter water from above Layer too dense => entrain lighter water from above Layer too light => entrain denser water from below Layer too light => entrain denser water from below Maintain finite layer thickness in upper ocean but allow massless layers on sea floor Maintain finite layer thickness in upper ocean but allow massless layers on sea floor Minimize seasonal vertical migration of coordinate layers by keeping non-isopycnic layers near top of water column. Minimize seasonal vertical migration of coordinate layers by keeping non-isopycnic layers near top of water column.

26. The hybrid coordinate is one that is isopycnal in the open, stratified ocean, but smoothly reverts to a terrain-following coordinate in shallow coastal regions, and to pressure coordinate in the mixed layer and/or unstratified seas. FloridaFloridaFloridaFlorida Cuba Cuba 

27. z σ-z σHybrid

28. 2007 LOM WorkshopBergen, Norway - Aug. 200728 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 Observations A hierarchy of Numerical Models, including HYCOM, is being used for developing an Ocean Prediction system in Brazil.

29. 2007 LOM WorkshopBergen, Norway - Aug. 200729 For the Near Future

30. Example for global: Hide coordinate poles over land Honrizontal Grid Structure Choices

31. CUBE SPHERE

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

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

34. Re=8000

36. Initially approx. 1/4 degree everywhere - here approx. 1 – 1/30 ° Elements ≈ 65,000 ICOM

37. Second Generation Horizontal resolution: 0.3-1.0 km in the coastal region;Horizontal resolution: 0.3-1.0 km in the coastal region; Generalized terrain-following coordinates: 46 layers: 10 uniform layers in the surface and bottom boundary layers, respectively.Generalized terrain-following coordinates: 46 layers: 10 uniform layers in the surface and bottom boundary layers, respectively. 1500 m cutoff off Georges Bank1500 m cutoff off Georges Bank Capable to nest to the coasta-estuarine model with a horizontal resolution of ~10 - 500 m;Capable to nest to the coasta-estuarine model with a horizontal resolution of ~10 - 500 m; Third Generation Horizontal resolution: 0.5-1.0 km in the coastal region;Horizontal resolution: 0.5-1.0 km in the coastal region; Sigma-coordinates: 31 vertical layersSigma-coordinates: 31 vertical layers 300 m cutoff off Georges Bank300 m cutoff off Georges Bank FVCOM UNSTRUCRURED GRID (Chen, UMASSD) Gulf of Maine

38. Second Generation Third Generation Surface sigma level: does not resolve the near-surface current because the horizontal velocity is calculated at the mid-point of the first sigma layer, which changes with depth. At the 2-m below the surface: Resolve the near-surface current better with the thin uniform layers at the surface..

39. Closing comments Models continue to evolve, with new ideas presently being developed Models continue to evolve, with new ideas presently being developed –Generalized vertical coordinates –Novel horizontal grids –Numerical methods (time stepping, advection operators, etc)‏ –Subgrid scale parameterizations Carefully choose your model (both code as well as resolution and parameterization) to have an a priori notion of what “ocean” will be simulated Carefully choose your model (both code as well as resolution and parameterization) to have an a priori notion of what “ocean” will be simulated