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FOAM Model Description
Contents
FOAM Products
The FOAM system produces 5-day forecasts of three-dimensional ocean temperatures, salinities and currents and sea-ice properties on a routine daily basis. It assimilates temperature profile data, surface height data from satellite-borne altimeters and satellite and in situ surface temperature data and is driven by six-hourly surface fluxes from the Met Office’s numerical weather prediction (NWP) system. High-resolution model configurations are nested inside the global configuration. Statistics on the differences between the model forecasts and observations are routinely produced and re-analyses can be generated from 1997 onwards.
The FOAM configurations that are presently run on a routine daily basis within the operational suite at the Met Office cover the globe with a 1° grid; the Atlantic and Arctic Oceans and the Indian Ocean with 35 km grids; and the North Atlantic, the Mediterranean Sea and the Arabian Sea with 12 km grids. An Antarctic configuration with a 27 km grid is also run on a daily basis and is to be transferred into the operational suite in the first half of 2005. All of these configurations have 20 vertical levels. The global, Atlantic and Arctic, and North Atlantic configurations are illustrated below.
Six-hourly full-resolution surface-flux fields from the global forecasts by the Met Office's NWP system to five-days ahead are currently used to drive all the FOAM configurations (in future fluxes from limited-area forecasts will drive some configurations). The flux fields used are the wind stress (vector with two components), wind mixing energy, penetrating heat flux, non-penetrating heat flux and precipitation minus evaporation. The NWP system calculates fluxes over sea-ice and open water ('leads') separately and combines them using sea-ice concentration analyses generated by NCEP. The surface temperature and salinity fields are also weakly relaxed towards the monthly Levitus et al (1998) climatologies.
Input Data
The global configuration is also driven by climatological monthly river inflow data from the Global Runoff Data Centre (GRDC) with the outflows from the largest 20 rivers adjusted to accord with Baumgartner & Reichel (1975).
Temperature and salinity profile data are assimilated at all depths. In the operational system the data are obtained from BATHY, TESAC and BUOY messages distributed by the Global Telecommunication System (GTS). These message formats are used to report expendable bathythermograph (XBT) data reported by Voluntary Observing Ships (VOS), and data from the Argo profiling floats and TAO/Triton equatorial moorings respectively. Quality control checks on these data include track, stability, background and buddy checks (Ingleby & Huddleston 2004).
Altimeter data from the Jason-1, Envisat and Geosat Follow-On (GFO) satellites are assimilated in all but the global configuration using products supplied twice a week by Collecte Localisation Spatiale (CLS) in Toulouse.
In situ surface temperature data from ships and drifting and moored buoys are assimilated. At present only advanced high-resolution radiometer (AVHRR) data on a coarse grid (2.5 degree spacing) are assimilated. All these data are distributed by the Global Telecommunication System (GTS). We will upgrade to using GODAE High Resolution SST (GHRSST) satellite data products when they become available.
Sea-ice concentration fields supplied by the Canadian Met. Centre (CMC) on a daily basis are also assimilated. These fields are based on SSM/I (special sensor microwave imager) data processed using the York/AES algorithm (Ramseier et al. 1988).
Dynamics
Storkey (2004) provides an excellent summary of the formulation of the physical ocean and sea-ice models used by FOAM in July 2004. The ocean model code, which originated from the Bryan-Cox code (Bryan 1969, Cox 1984), is developed jointly with groups in the Hadley Centre who use it for climate prediction. The FOAM formulation is quite close to that used by HadCM3 (Gordon et al. 2000).
Various bathymetries (Smith & Sandwell 1997, DBDB2 and GEBCO) have been used in building the present configurations. The bathymetry after interpolation to the model’s grid is smoothed twice using a 1-4-1 filter. Grid-scale holes are filled to avoid an instability (Pacanowski & Griffies 1999) which appears to be associated with the B-grid staggering of variables and the depth and width of important channels are adjusted using Thompson (1996) as a reference. At open boundaries of nested models the bathymetry in the relaxation zone (see below) is reset to be as similar as possible to the model providing its boundary data. Tests of the impact of code to achieve a smoother bathymetry using partial bottom cells (Pacanowski & Gnanadesikan 1998) are in progress.
The limited area models use the Flow Relaxation Scheme (FRS) (Davies 1983, McDonald 1997) as boundary conditions for all prognostic variables (including temperature, salinity and horizontal velocity components). This relaxes the model fields in the inner model towards those in the outer model over a relaxation zone typically 4-8 gridpoints wide, the strength of the relaxation increasing as the outer edge of the inner model is approached. (When FOAM transitions to a free-surface we will transition to Flather conditions for the external modes.) Most of the limited area models use a rotated latitude-longitude grid to achieve for given resolution the largest minimum grid-spacing Dx. This allows a longer time-step to be used. At present resolutions it has been found that the maximum model timestep Dt is limited by the CFL criterion
2(c + u) Dt < Dx
in which is the speed of fastest internal waves (about 3 m/s), is the fastest advecting velocity in the model and the factor of 2 arises from the use of the leapfrog scheme.
The prognostic equation for horizontal momentum is similar to that in the Bryan-Cox code except that the advection of momentum uses the Webb (1995) scheme and a simple quadratic bottom friction is used to crudely parametrise tidal mixing. To increase the timestep that can be used the Coriolis term is calculated semi-implicitly in coarser-resolution configurations, and the pressure gradient is averaged across timesteps in higher-resolution configurations (Brown & Campana 1978). A combination of harmonic and biharmonic viscosities is used to damp gridscale noise and westward migrating eddies. The choice of parameters has a significant impact on the model simulation (Chassignet & Garraffo 2001). The barotropic flow is represented by a streamfunction using the rigid-lid approximation (see Storkey 2004 for details).
The prognostic equation for tracers presently uses a form of third-order upwind advection similar to Holland et al. (1998). A combination of a less diffusive advection scheme and the thickness diffusion scheme of Gent & McWilliams (1990) is being trialled as an alternative. The Griffies et al. (1998) formulation of isopyncal diffusion is employed.
The formulation of vertical mixing is explained by Gordon et al. (2000) and Storkey (2004). Momentum and tracers are mixed using the Pacanowski & Philander (1981) scheme and a simplified form of the Large et al. (1994) scheme. In addition tracers are mixed using a mixed-layer energetics scheme based on Kraus & Turner (1967) and Davis et al. (1981). Convective adjustment of tracers is performed by applying the Roussenov scheme (Roether et al 1994) followed by the Rahmstorf (1993) scheme.
The thermodynamic component of the sea-ice model uses the zero-layer model of Semtner (1976) and Hibler’s (1979) formulation for leads processes. The dynamic component is based on Bryan et al. (1975): the ice concentration is advected using the top-level ocean currents and smoothed using Laplacian diffusion. The EVP formulation of Hunke & Dukowicz (1997) and ice thickness distribution scheme of Lipscomb et al. (2001) are being trialled.
Assimilation Methods
Data assimilation is based on a new version of the analysis correction (a/c) scheme. The a/c scheme was originally devised by Lorenc et al. (1991) and implemented for FOAM by Bell et al. (2000a). The new version (Bell et al. 2003) provides a sub-optimal approximation to a variant of 4D variational assimilation. Analysis steps are performed once per day. Each observation makes its full impact on the model on the day it arrives and on subsequent days is taken into account by giving additional weight to the model at the observation’s location. Each analysis step consists of a number of iterations. On each iteration the observations are separated into groups which are easily related (thermal profiles, saline profiles, surface temperature, surface height). For each group of observations (e.g. the temperature profile data), increments are calculated first for the directly related model variables (e.g. the temperature fields). These increment fields are then used to calculate increments for less directly related model variables (e.g. the velocity fields) using hydrostatic and geostrophic balance relationships, water property conservation or statistical relationships. These balancing increments make the analysis multivariate. Increments are also made to the observations (Bratseth 1986) so that the iterations converge towards the statistically optimal analysis. The univariate components of the model error covariance are specified as the sum of two 3D error covariances, one describing the ocean mesoscale, the other large scales including atmospheric synoptic scales (Martin et al. 2002). These and the observation error covariances are estimated from statistics of observation minus model values obtained from hindcast assimilations. Altimeter data are assimilated by displacement of isopycnal surfaces (an extension of the Cooper & Haines 1996 scheme). A pressure correction technique (Bell et al. 2004) is employed to improve the dynamical balance near the equator (see section 3.1) and analyses performed with large correlation scales are used to attempt to remove large-scale biases in the AVHRR surface temperature data.
Assessments
It has been found that the assimilation of temperature and salinity data below 1,000 metres depth can have major impacts on the barotropic flow and the meridional overturning in the FOAM system. The version of the FOAM system implemented in 1997 deliberately excluded observational data below 1,000 metres depth because of the deleterious impact of occasional deep observations in the Gulf Stream region (Bell 1994). With the advent of the Argo system it is highly desirable to assimilate both temperature and salinity data at all depths (see next sub-section). It is important for the quality control of the Argo data to detect suspect observations, particularly those with depth independent offsets.
The figure below shows the impact on verification statistics of assimilating Argo profile data into the FOAM 1° model. The statistics are root mean square differences between profile observations and model fields valid the day before the observations (i.e. fields in which the observations have not been assimilated). All the model integrations covered the period January to May 2003, were forced by 6-hourly NWP fluxes and were started from the operational analysis for 1st January 2003. A 'control' integration assimilated no data; a second integration assimilated only salinity profile data from Argo; a third assimilated only temperature profile data from Argo and the final integration assimilated both temperature and salinity profile data. No other data were assimilated and an early version of the new assimilation scheme was used.
References
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(Last Updated: 01-08-2008)