Basics of numerical oceanic and coupled modelling Antonio Navarra Istituto Nazionale di Geofisica e Vulcanologia Italy Simon Mason Scripps Institution of Oceanography USA

Sea Ice Oceans The Climate System Biosphere Soil Moisture Run-off Atmosphere Precipitation Evaporation

Oceans -- Soil -- Cyosphere -- Biosphere COOLING HEATING Latent Heat Wind Stress RAIN EVAPORATION Sensible Heat REFLECTION EMISSION ABSORPTION TRANSPORT PRESSIONE Radiation Temperature Water Vapor TRANSPORT Solar Radiation Earth Radiation Wind

Ocean Models All atmospheric GCMs have some form of ocean component, and all ocean models have some form of atmospheric component. Hierarchy of complexity: swamp ocean slab ocean detailed mixed-layer dynamical ocean

Atmosphere Latent Heat Flux Wind Stress RAIN EVAPORATION Sensible Heat TemperatureCurrents TRANSPORT Solar Radiation Salinity TRANSPORT Atmospheric radiation Density

Dynamical Models Important differences between ocean and atmosphere:

Dynamical Models Important differences between ocean and atmosphere: Confined to only certain areas of the earths surface. Spectral representation is not used.

Dynamical Models Important differences between ocean and atmosphere: Confined to only certain areas of the earths surface. Many of the important ocean models in climate prediction are basin or sub-basin scale. Spectral representation is not used. Smaller spatial scale of oceanic eddies compared to atmospheric eddies; also most transport is in relatively narrow ocean currents. Grid resolution needs to be much finer than in atmospheric GCMs.

Dynamical Models Important differences between ocean and atmosphere: Confined to only certain areas of the earths surface. Spectral representation is not used. Smaller spatial scale of oceanic eddies compared to atmospheric eddies; also most transport is in relatively narrow ocean currents. Grid resolution needs to be much finer than in atmospheric GCMs. Much poorer observational data. Problems for initialization, verification, and parameterization

Dynamical Models Spatial scale: eddy resolving models less than 0.25 resolution. non-eddy resolving models are at about 2. higher resolution required near equator, and near the poles where currents are narrower. the coarser models are used in the fully coupled models.

Dynamical Models Initialization: Problematic because of lack of observations (mainly SSTs and surface height), very little sub-surface measurements, cf. atmospheric initialization given only surface data. Spin-up the model using observed wind stress. Need to improve assimilation schemes – many ocean models initialized with zero motion.

The BMRC Coupled Model t=0 Forced Ocean Model obs, SST obs,... Assimilate Ocean Data: T(z),,... FSU/BoM Winds BoM SST, S LEV O G C M A G C M F O R E C A S T

Coupling Start of integration Coupling Integrate the coupled model for a period, e.g. two years, but impose observed surface temperature and salinity Start of integration Coupling Spin-up the ocean with observed atmospheric forcing Robust Diagnostic Spin-up But sometimes the models are simply started from climatological conditions or, in the case of climate change experiments, the procedure may become much more sophisticated to account for effects from soil and ice.

Oceans -- Sea Ice Atmosphere Wind StressPrecipitation Solar Radiation Atmospheric Radiation Air Temperature Sea Surface Temperature Sensible Heat FluxLatent Heat Flux Wind StressFresh Water Flux Surface Temperature COUPLER: (1) Interpolate from the atmospheric grid to the ocean grid and vice versa. (2) Compute fluxes

Very Large Compiuters are needed Project of the Earth Simulator Computer (Japan) : objective, a global coupled model with 5km resolution

The main problem is how to synchronize the time evolution of the atmosphere with the evolution of the ocean. The most natural choice is to have a complete synchronization (synchronous coupling): This choice would require to have similar time steps for both models, for instance 30min for the atmospheric model and 2 hours for the ocean model. Computationally very expensive Atmosphere Ocean Coupling t t t t t t t t

Another possibility is to exploit the different time scales using the fact that the ocean changes much more slowly than the atmosphere (asynchronous coupling): Atmosphere Ocean Coupling t Integrate for a very long time This choice save computational time at the expense of accuracy, but for very long simulations (thousands of years) may be the only choice. Coupling t Integrate for a very long time

Sea Surface Temperature High marine temperatures in the model are too narrowly confined to the equator, in the observations the warm pool is wider Observations Model Coupled models can reproduce the over-all pattern, but they tend to be warmer than observations in the eastern oceans and colder in the western portions of the oceans

Dynamical Models Systematic bias is a major problem with dynamical ocean models (including coupled models). Errors in the annual cycle Climate drift - the systematic bias depends on the forecast lead-time.

Forecast model bias A comparison of the coupled model 12 month Nino3 forecasts [top panel] for February (blue), May (red), August (green), and November (brown) initial conditions average over all years, compared with climatology (purple). The bottom panel show the bias relative to this climatology.

Conclusion Really, there should be no conclusion. We have only started to understand the behaviour of coupled models and there is still a long way to go.