Numerical Models of Oceans and Oceanic Processes

Transcription

1 Numerical Models of Oceans and Oceanic Processes Kantha and Clayson, 2000; review notes by S. P. Muszala 1 Introduction to Ocean Dynamics first numerical baroclinic ocean model Kirk Bryan, late 1960 s due to high heat capacity of water, (2.5m of upper ocean == entire troposphere) oceans cover 70% of Earth surface oceans act as thermal flywheels reservoirs of CO times CO 2 than in the atmosphere residence time of about a millenium play important role in determining climate conditions disruptions in global meridional thermohaline circulation may have changed earth climate in the past ENSO (El Nino-Southern Oscillation) causes widespread precipitation changes... atmosphere-ocean coupling oceanography is data-poor. remote penetration to about 100m water depth. rely on sparse in situ observations. ocean motions turbulent and span large spatial and temporal scales. ocean circulation due to these: density structure of water masses composing ocean basins radiative fluxes at its surface forcing (wind stress and buoyancy fluxes) imposed at ocean surface by atmosphere (also tide-forces due to moon and sun). temporal - hourly to decadal and beyond spatial - kilometer scales (atmospheric front) to basin scales. ocean features deep abyssal plains

2 shallow shelves mid-ocean ridges and island chains narrow passageways and straits and their circulations (western boundary currents) broad gyres spanning basins equatorial current system antarctic circumpolar current that connects various basins. Salient Features physical characteristics of global ocean determined by continental drift. continental (lithospheric) plates move approx. cm/yr. ocean crust created at MORs mantle hot spots create island chains. factors of ocean dynamics MORs island chains submerged guyots seamounts deep trenches play minor role so models usually truncate at bottom depth in abyssal oceans (5000m). continental shelves associated with sedimentary processes. circulation on shelf forced strongly by winds and astronomical tides. density gradients and winds play important role in circulation in deep basin. model shelf and basin proper separately with different ocean models. slope/basin transition difficult to model but important to hydrocarbon exploration. shape and depth distribution important to ocean circulation modeling circulation in paleo-ocean. studies difficult. submarine earthquakes and slumps generate tsunamis. only dynamic geologic activity that is important to ocean modeling. 2

3 three primary ocean basins. connected in so. hemi. by souther ocean around the antarctic subcontinent. pacific and atlantic connected by arctic ocean by straits. pacific and indian connected via straits in indonesian archipelago (very important for heat and salt flux from pacific to indian ocean). pacific atlantic indian Mean Circulation horizontal circ. in each basin driven mostly by surface forcing applied by overlying atmosphere. equatorial mid-high latitudinal rate of mechanical work done by wind on oceanic general circulation dominated by action of zonal wind stress component on the zonal component of the gsostrophic current. equatorial circulation in each basin consists of complicated pattern of currents and counter-currents driven by curl of the wind stress. superimposed on this are fluctuations driven by fluctuating wind forcing. Indian Ocean circulation differs because 1) its limited meridional extent 2) seasonally reversing monsoon winds. 3-5 year timescales - pacific ocean dominates the weather and climate centuries and beyond timescales - atlantic ocean dominates weather and climate. meridional thermohaline circ. important to long-term climate. Indonesian Throughflow is only low latitude connection between ocean basins at present. impacts tropical and global climate. important to thermohaline circulation. stable stratification in interior of oceans due to two things. 1. cold deep and intermediate water formation in subpolar seas 2. subduction of water masses in vicinity of poleward limbs of the sub-tropical gyres. 3. arctic ocean circulation dominated by perennial ice cover. 4. ice sheets (5% earth surface) and glaciers largest reservoirs of freshwater on earth. 5. oceans play an important role in geochemical evolution of the earth. 6. primary biological production conditional upon simultaneous availability of solar insolation and inorganic nutrients dissolved in the water. 3

4 Modeling Issues aspect ratio of oceans and atmosphere are small. H=4KM (10KM) L=1000KM(1000KM). H/L=10 3. Vertical velocity W = 10 4 m/s to 10 5 m/s and horizontal velocity, U is 10 1 m/s. In areas of deep convection W can reach several cm/sec. basin scale and global models often ignore or simplify surrounding shelves and marginal seas. Coupled ocean-atm. model essential for simulations and estimations of oceanic state over timescales longer than weeks. air-sea exchange of momentum, heat and fresh water important in coupled models. Comparison with the Atmosphere differences in driving mechanism and in scales of motion. general GFD texts deal with ocean and atmosphere. principal difference between Ocean and Atm. the way they are driven. Atm. heated mainly from below...some bulk heating occurs near top of and above tropopause. solar radiation passes through amos. envelope and heats ground and water surfaces which in turn transfer heat to the atmosphere. heat loss occurs throughout the atmospheric column by radiation to space. differential cooling of continental masses and ocean masses drive large scale circulation (mostly horizontal). vertical motions occur in localized regions. oceans driven at the surface by atmospheric winds and fluxes. solar heating confined to thin layer at surface. heat loss must also occur at the surface. oceans don t have anything akin to differential heating due to cloud cover. oceans have long temporal time-scales (long memory). Atm. short temporal scales except in stratosphere where chemical constituents can have residence times of many years. Atm. changes in radiative balance in column and phase conversion involving water vapor and clouds and attendant latent heat absorption and release cause changes in atmospheric circ. Ocean changes in surface forcing that primarily drive oceanic variability. Rossby waves propagate much more slowly in the oceans. Boussinesq approximation adequate in oceans. atm large density variations. ocean small density variations. rossby radius of deformation, 1000km in atm, 40km in midlat. oceans. 4

5 oceans constraints imposed by meridional boundaries. atm. lack of obstructions due to zonal flow (except some midlatitude mountain chains). basins unique to oceans. modeling thermohaline circ. really difficult. 1.1 Types,Advantages, and limitations of ocean models Global or regional doubling resolution on 3-D model order of magnitude increase in computational power. regional models how to tell model about state of the rest of the ocean (suitable conditions along open lateral boundaries) best soln. is to embed high res. mesh in low res. mesh. Deep basin or shallow coastal circ. in shallow coastal regions is highly variable, driven by synoptic wind and other rapidly changing surface forcing (near river outflows, buoyancy diffs between fresh river water and saline ambient shelf water. mixing physics and resolution of bottom boundary layer important to coastal models. deep basins sluggish. horizontal density gradients below wind-mixed upper layers important factor for circulation (deep basins). MOM2 z-level model with/with-out upper mixed layer. good for ocean basins. z-level model eulerian approach. variables at each level and each point on horizontal model grid are solved. semi-lagrangian approach - divides ocean vertically into layers and models variations of properties at each grid point on horizontal grid. rigid lid or free surface oceanic response to surface forcing 1. fast barotropic response mediated by external kelvin and gravity waves on sea surface (short timescales). 2. relatively slower baroclinic adjustment via internal gravity, kelvin, planetary rossby and other waves (long timescales). rigid lid allows larger time stepping of a model. suppresses external forcing. models long timescale stuff. climate models. rigid-lid are no longer advantageous for either computational efficiency or modeling dynamics. shallow water apps. storm surge and tide modeling need free-surface model and dynamics. 5

6 hydrostatic, quasi-hysrostatic, or nonhydrostatic almost all large scale circulation models based on hydrostatic form of the incompressible Navier-stokes equations. fully nonhydrostatic models can be used at all horizontal resolultions...computationally intensive. Comprehensive or purely dynamical comprehensive include changes in density over time. purely dynamical doesn t include density changes over time only investigate changing wind forcing. With applications to short-term simulations or long-term climate studies climatic timescales important to model thermohaline circulation. long-term climate studies require multi-teraflop computing capability. Quasi-geostrophic or primitive equation based QG models assume balance between coriolis and pressure gradient in dynamical equations. allows longer timesteps. not very accurate. becoming obsolete. Intermediate models (PE and QG) are becoming the norm. retain higher order terms in Rossby number expansion or the governing equations. barotropic or baroclinic barotropic model density gradients are neglected...currents become independent of depth in water column. barotropic model can accurately model tidal sea surface elevation fluctuations and storm surges. order of magnitude less computational resources that comparable baroclinic model. baroclinic model important when modeling vertical structure of currents or the density field. process studies-oriented or applications-oriented models used to study a specific process can be simplified. computationally less expensive. need less observational data for model initialization. applications-oriented models need extensive observational data for realistic initialization, forcing and data assimilation. assimilation important for realistic nowcast, forecast and hindcast apps. similar to numerical weather prediction models in atmosphere. 6

7 with and without coupling to sea ice sea ice insulates the ocean from cold atmosphere during the winter and mediates the exchange of heat and momentum between the two. plays an important role in polar and sub-polar seas. most models only approximate sea ice although comprehensive ice-ocean coupled basin models of the arctic exist. coupled to the atmosphere or uncoupled for accurate long timescale processes it is necessary to couple ocean and atmosphere. eg. forecasting El Nino. 9 Sigma-coordinate Regional and Coastal Models 9.1 Introduction structured grids are least flexible for coastal models finite elements are most flexible but have some computational and numerical cost require explicit free surface dynamics solve for both temp. and slinity. must be careful with nonlinear advective terms. parameterization of subgrid scales is not explicitly simulated by the finite resolution of the model. horizontal diffusion terms used for numerical reasons...chosen to give best solution. distinguishing characteristics of shallow oceans 1. free surface dynamics 2. vertical mixing 3. bottom boundary layer 4. tides and tidal mixing 5. storm surges Haidvogel and Beckmann (1998) three test cases for coastal models 1. Gravitational adjustment problem fluids of two different densities are separated by a vertical wall. wall is removed. lighter fluid spreads over the over and a two-layer stably stratified system results. advection schemes that assure positive definiteness do a better job at maintaining a clear front boundary. 7

8 2. Barotropic flow over a coastal canyon a time-varying, along-coast wind stress is applied over a coastal shelf/slope with an imbedded canyon. z-coordinate models fared pretty poorly here. 3. baroclinic flow over a coastal canyon. this problem combines strong stratification and steep topography...difficult for all models. x-level model required the most smoothing. coastal models have an advantage when using a vertical coord. system that conforms to the ocean bottom. rest of this chapter deals with CUPOM. 9.2 Governing Equations use hydrostatic and Boussinesq approximations. horizontal diffusion can be simplified since there is a great deal of uncertainty associated with the choice of horizontal mixing coefficients and the horiz. mixing terms are regarded as a numerical necessity to control the subgrid scale energy pileup. need to avoid spurious vertical mixing due to horizontal mixing. 9.3 Vertical Mixing vertical mixing much better understood than horizontal mixing region below active mixed layer is a region of strong static stability, but it is also strongly sheard, so that turbulence here is intermittent. It is difficult to model but unwise to ignore the effects. 9.4 Boundary Conditions boundary conditions must be met at bottom, free surface, and lateral boundaries. ocean bottom is impermeable fluxes of momentum, net heat and salt at free surface and the bottom have to be perscribed. fluxes of turbulent quantities must be perscribed or the quantities themselves. have to specify SW solar insolation impinging on the ocean surface. 9.5 Mode Splitting Separates external and internal mode equations. solves external modes at time steps cfonsistent with the fast external gravity waves. solves internal modes at larger time steps which are consitant with slow internal gravity wave speeds. 8

9 9.6 Numerics use second order finite difference scheme implicit in the vertical, explicit in the horizontal. should be implicit in the vertical so as not to impose sever time step limitations that could be brought upon by vertical grid sizes Vertical Direction Horizontal Direction 9.7 Numerical Problems 9.8 Applications 9.9 Code Structure 9