An "off-line tracer model" is one in which only the tracer is a prognostic variable, other quantities such as velocity fields, mixing and convection are inputs into the model. The off-line simulation of the oceanic transport of tracer requires the combination of two computational tools. The first is the ocean general circulation model (OGCM), which defines the grid resolution, and the speed and direction of ocean currents. The second is the tracer dispersion model, which computes the effects of advection and mixing on the tracer using a prescribed source functon and the velocity data set from the OGCM.
2.1 Ocean General Circulation Model
The velocity fields used to determine the advective transport of the tracer in this study are obtained from the Parallel Ocean Climate Model (POCM), which is a descendent of the Semtner and Chervin (1992) global model. This model simulates ocean circulation for the majority of the world's oceans, excluding the Arctic Ocean (to avoid grid convergence problems). It is forced using the European Centre for Mid-Range Weather Forecasting (ECMWF) model reanalyses over a 20-year period from 1979 to 1998. The algorithms used to simulate ocean dynamics are adapted from the Geophysical Fluid Dynamics Laboratory (GFDL) Modular Ocean Model (Bryan, 1969; Cox, 1984; Pacanowski et al., 1991).
The POCM has an average horizontal resolution of 1/4o latitude and longitude over a Mercator grid; thus finer longitudinal resolution is defined at higher latitudes. In the most important latitudinal domain of this study (approximately 40oS to 0o) longitudinal resolution is 0.4o, which corresponds to a range of 34 km at mid-latitudes to 44 km at low-latitudes. The latituinal resolution also varies from 0.31o (34 km) at mid-latitudes to 0.4o (44 km) at low-latitudes. The model divides the vertical dimension of the ocean into 20 geopotential depth levels. These range in thickness from 25m in the top 100m up to 400m at the bottom (5500m).
The advection fields used in this study were derived from mean monthly velocity fields over the full 20 year model run. This allowed computation of long term annual, monthly mean, and interannually varying velocity fields used in the tracer experiments.
2.2 Simulated Ocean Dynamics
Figure 1a shows the annual-mean modelled surface circulation of the South Pacific Ocean. The major currents of the surface circulation of the South Pacific Ocean, including the sub-tropical anticyclonic gyre, the equatorial current system and the western boundary current (the East Australian Current, EAC), are well represented by the model. The overall transport is summarised in the mass transport stream function shown in Figure 1b. This shows depth-integrated flow patterns in units of Sverdrups (1Sv = 106msec-3). Clearly apparent is the subtropical gyre in the South Pacific Ocean, with the EAC transporting 30 Sv polewards. Near Moruroa, whilst surface flow is eastward, the interior ocean circulation from 1000 - 260m depth is westward.
We have compared surface currents from the POCM with available observational data (Hansen and Poulain, 1996) measured from drifting buoys. The model reproduces the direction and magnitude of the circulation in this region, on a seasonally-varying and annual-mean scale. Most relevant to our study, the eastward surface drift observed in the POCM in the region of Moruroa Atoll is confirmed by the buoy data. Other major features of the surface circulation such as the EAC and the equatorial current system also show agreement between model and observations.
Measurements of the circulation in the South Pacific Ocean at depths below the wind driven surface layer are very sparse. Reid (1986) has described the circulation at all depths using available patterns of tracers (temperature, salinity, oxygen, silica and helium-3) and density. This general description is well represented by the model. At depths of 300m to 1400m, currents in the tropical South Pacific flow in a general westerly direction, with the southward flowing western boundary current completing the circulation. The southern extension of the westerly current increases with depth as observed. The seasonal variability is reduced in the oceanic mid-depths, being driven by larger scale, long-term thermohaline forces and geostrophy (Tomczak and Godfrey, 1994). The effects of interannual climate variations can however, still be apparent at mid-depths, with a decrease in westward current velocity occurring during the 1982-1983 ENSO event.
Figure 2 shows average horizontal ocean currents over a 5o grid centred at Moruroa Atoll. These near-source currents will advect the initial radionuclide tracer released in the model runs. Current velocities are generally zonal, with eastward flow in the upper 200m, and westward flow at mid-depth. A southerly component is also apparent in the uppermost layer. Seasonal and interannual variations in currents are apparent in the upper 100m and strongest at the surface. At mid-depths interannual current variability is apparent, whilst seasonal variations are weak.
2.3 Tracer Dispersion Model
The effects of advection and dispersion on the radioactive tracer are computed using an off-line tracer model. The model is an adaptation of the GFDL Modular Ocean Model (Bryan, 1969; Cox, 1984; Pacanowski et al, 1991), using its tracer conservation component in combination with other features. The GFDL model is a three-dimensional primitive equation ocean model designed as a flexible tool for ocean and coupled climate modelling. Advection and mixing of the tracer within the model is described by the three-dimensional tracer conservation equation
(1)
where (x,y,z) is Cartesian space, t in time, (u,v,w) the three components of velocity, KH the horizontal mixing coefficient, KV the vertical mixing coefficient, Q the tracer concentration, QS the tracer source, and QD the decay/sink of tracer. This tracer conservation equation therefore relates any change in the concentration of the tracer to changes due to the three components of advection and mixing, as well as source/sink terms.
The horizontal components of velocity (u,v) are obtained from the POCM for each grid-box and each month of interest. The vertical component of velocity (w) is determined diagnostically from the continuity equation
(2)
The source terms refer to the release of tracer into the simulated ocean, which has temporal, geographic and quantitative parameters that are defined separately for each tracer experiment.
A time step of eight hours was adopted in this study. This value is a comprimise between computational efficiency and numerical considerations. It is short enough to avoid 'overshoots' of tracer across a single grid box, occurring when the advective distance of tracer exceeds the grid resolution within a single time step. It is also sufficient to avoid excessive numerical diffusion downstream of the tracer signal.
Mixing terms are required within the tracer model to account for physical processes that affect the transport of the tracer which occur at scales below the resolution of the model, and to partly mimic those lost by averaging over a monthly time scale (e.g. transient eddies). The POCM resolves ocean dynamical processes at the mesoscale (tens of kilometres in the study domain) and above (e.g. gyres, western boundary currents, deep ocean jets, and so on). This degree of resolution incorporates eddy mixing in prognostic mode, which accounts for the majority of the kinetic energy transfer within the ocean (Tomczak and Godfrey, 1994). However, some of the mixing at this scale is unresolved after velocity fields have been averaged. Other ocean dynamical processes that require parameterisation include boundary turbulence, internal wave breaking, vertical convection and velocity shear (England and Oke, 2001). Within the three-dimensional structure of the model, these processes are simply approximated as horizontal and vertical mixing terms.
The parameterisation of mixing presents a degree of uncertainty within the tracer model. Horizontal mixing in the ocean is largely dependent upon eddy activity, density structure, and the resultant turbulence and velocity shear created between water masses moving at different velocities. While the POCM partly resolves the mixing created directly by the eddy advection in prognostic mode, this study uses the averaged monthly and annual velocities, which filter out smaller scale transient eddies. As such, the associated turbulence and velocity shear must be parameterised. Regions that experience high levels of eddy activity, such as western boundary currents (WBC) and the Antarctic Circumpolar Current (ACC) will have higher levels of horizontal mixing. Methods for indexing the horizontal mixing coefficient to the degree of eddy activity are a relatively recent ocean modelling development (see, e.g., Rix and Willebrand, 1996; Visbeck et al, 1997), and are yet to be incorporated into this tracer model. Horizontal mixing has thus been restricted to a uniform value on the basis of some preliminary testing of the model with different values for the horizontal mixing coefficient. A relatively low value of KH = 105 cms-2 was adopted on the basis of low eddy activity within the study region, as shown by drifting bouy data (Hansen and Poulain, 1996) and sea surface altimetry (Stammer et al., 1996). Sensitivity tests undertaken revealed minimal change in simulation for smaller values of KH.
Vertical mixing in the surface layer of the ocean is enhanced by wind forcing, which generates turbulence and breaking waves. Below this depth vertical mixing is of a smaller magnitude, and is influenced by the degree of density stratification and the roughness of the seafloor bathymetry (see e.g. Polzin et. al., 1997, Toole et. al., 1994). Vertical mixing in our tracer model has been configured based upon the widely used Bryan and Lewis (1979) formula that approximates mixing as a function of depth. This formula is still used in state-of-the-art climate model simulations (e.g., Manabe and Stouffer, 1996; Hirst et al., 2000) and was originally based upon direct estimates of vertical mixing rates in the ocean (Gregg, 1977; Rooth and Ostlund, 1972). For the purposes of our study, it is a reasonable approximation of mixing in the open South Pacific Ocean near Moruroa Atoll.
http://www.maths.unsw.edu.au/~doughaze Page created by Douglas R. Hazell 7/6/2001 Last update of this page: 1/8/2001