FOAM System Description
The FOAM system consists of the following components which are described in the subsequent sections.
- Physical ocean model
- Sea ice model
- Data assimilation scheme
- Observation processing system (quality control)
The Forecast Ocean Assimilation Model (FOAM) system uses the Nucleus for European Modelling of the Ocean (NEMO; Madec 2008) model as its hydrodynamical core. NEMO is a pan-European community ocean modelling framework owned and maintained by a consortium of institutes including the Met Office. It has a large user community and is used at a number of research and operational forecasting centres. NEMO also forms the ocean model component of the Met Office seasonal forecasting (GloSea: MacLachlan et al., 2014) and climate modelling (HadGEM: Hewitt et al., 2011) systems.
The Global FOAM system is based on the GO5 configuration described by Megann et al. (2014) which was developed in the UK under the NERC-Met Office Joint Ocean Modelling Programme (JOMP). The model grid is the ORCA025 system developed at Mercator Océan (Drévillon et al., 2008) which uses a tri-polar grid to avoid singularities associated with the convergence of meridians at the North Pole. The climatological river run-off fields for ORCA025 were derived by Bourdalle-Badie and Treguier (2006) based on estimates given in Dai and Trenberth (2002). The regional FOAM configurations were developed at the Met Office meanwhile use regular latitude-longitude grids with bathymetries based on the GEBCO 1 arc-minute dataset and climatologiocal rivers from the Global Runoff Data Centre (GRDC), Germany.
The vertical coordinate system is based on fixed geopotential levels ("z-levels") with partial cell thicknesses allowed at the sea floor. The vertical mixing uses the TKE scheme of Gaspar et al. (1990) which was embedded into NEMO by Blanke and Delecluse, 1993). This is a single-equation scheme with an algebraic expression for the mixing length based on the local density profile. A quadratic bottom friction boundary condition is applied together with an advective and diffusive bottom boundary layer for temperature and salinity tracers (Beckmann and Döscher, 1997). The model uses a linear free surface, and an energy- and enstrophy-conserving form of the momentum advection. The tracer equations use a TVD advection scheme (Zalesak 1979) and the diffusion operator is laplacian and along-isopycnal. The lateral boundary condition on the momentum equations is free slip for the global configuration and partial slip for the regional configurations. The horizontal momentum diffusion is bilaplacian for Global FOAM whilst the regional configurations use a combination of laplacian and bilaplacian operators.
The model is forced at the surface using the CORE bulk formulae scheme of Large and Yeager (2004) using fields provided by the Met Office Unified Model (UM) global Numerical Weather Prediction (NWP) system. These forcing fields consist of 3-hourly radiative fluxes, 3-hourly 10m temperature and humidity fields and 1-hourly 10m wind speeds.
The regional configurations are nested into the global configuration using one-way lateral boundary conditions with the Flow Relaxation Scheme algorithm (Engerdahl, 1995). Velocities and tracers are relaxed to outer-model values over a 9-point buffer zone at the edge of the model domain. The depth-mean component of the velocities at the boundaries is adjusted so that the total water volume in the model domain is conserved. In the North Atlantic configuration a relaxation to climatology is applied near the Strait of Gibraltar (which is closed in the model) to simulate the Mediterranean outflow water.
The sea ice component of FOAM is currently using the Los Alamos CICE model of Hunke and Lipscomb (2010) based on the HadGEM3 implementation of Hewitt et al. (2011). The CICE model determines the spatial and temporal evolution of the ice thickness distribution (ITD) due to advection, thermodynamic growth and melt, and mechanical redistribution/ridging (Thorndike et al., 1975). At each model grid point the ice pack is divided into five thickness categories (lower bounds: 0, 0.6, 1.4, 2.4 and 3.6 m) to model the subgrid-scale ITD, with an additional ice-free category for open water areas. At present the thermodynamic growth and melt of the sea ice is calculated using the zero-layer thermodynamic model of Semtner (1976), with a single layer of ice and a single layer of snow. However CICE allows the use of multi-layer snow and ice thermodynamics and these will be used in future versions of FOAM.
The calculated growth or melt rates are used to transport ice between thickness categories using the linear remapping scheme of Lipscomb (2001). Ice dynamics are calculated using the elastic-viscous-plastic (EVP) scheme of Hunke and Dukowicz (2002), with ice strength determined using the formulation of Rothrock (1975). Sea ice ridging is modelled using a scheme based on work by Thorndike et al. (1975), Hibler (1980), Flato and Hibler (1995) and Rothrock (1975). The ridging participation function proposed by Lipscomb et al. (2007) is used, with the ridged ice being distributed between thickness categories assuming an exponential ITD.
For Global and North Atlantic FOAM configurations the CICE model runs on the same grid as the NEMO ocean model with NEMO-CICE coupling as detailed in the HadGEM3 documentation (Hewitt et al., 2011). The Indian Ocean and Mediterranean Sea regional FOAM model do not include the CICE ice model owing to the lack of sea ice in these areas.
The data assimilation component of FOAM is performed using NEMOVAR (Mogensen et al., 2012). NEMOVAR is a multivariate, incremental 3D-Var, first guess at appropriate time (FGAT) data assimilation scheme that has been developed specifically for NEMO in collaboration with CERFACS (Centre Européen de Recherche et de Formation Avancée en Calcul Scientifique), ECMWF (European Centre for Medium-range Weather Forecasting) and INRIA-LJK (French Institute for Research in Computer Science and Automation–Jean Kuntzmann Laboratory).
The state vector in NEMOVAR consists of temperature, salinity, surface elevation, sea ice concentration and horizontal velocities. Key features of NEMOVAR are the multivariate relationships which are specified through a linearised balance operator (Weaver et al., 2005) and the use of an implicit diffusion operator to model background error correlations (Mirouze and Weaver, 2010). Assimilation of temperature and unbalanced salinity in the Global FOAM system is performed using multiple length scales whilst the regional models use a single length scale for all variables. The dual length scale formulation used for the Global FOAM configuration follows the methods described by Martin et al. (2007) in which a correlation function is constructed by linearly combining 2 separate correlation functions.
The NEMOVAR system includes various bias correction schemes for SST and altimeter data, and their implementations are detailed in Waters et al. (2013). The SST bias correction scheme aims to remove bias in SST data due to errors in the non-constant atmospheric constituents used in the retrieval algorithms by correcting data to a reference data set of assumed unbiased SST observations (Martin et al., 2007; Donlon et al., 2012). An altimeter bias correction scheme is used to correct biases in the mean dynamic topography (MDT) which is added to the sea level anomaly (SLA) altimeter observations prior to assimilation. The bias correction is applied in a similar way to Lea et al. (2008), by adding an additional altimeter bias field to the data assimilation control vector and including extra terms in the 3D-Var cost function. Systematic errors in the wind forcing near the Equator are counteracted by the addition of a correction term to the subsurface pressure gradients in the tropics to improve the retention of temperature and salinity increments by the model (Bell et al., 2004).
There is automated quality control of all data. The SST, SLA and sea-ice data is compared with the model background using the Bayesian procedure described in Ingleby and Lorenc (1993). The profile data are processed using the comprehensive method described in Ingleby and Huddleston (2007). The variances used in the quality control are the same as those used in the assimilation.
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(Last Updated: 26-11-2014)