# FOAM System Description

### Overview

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)

### Physical ocean model

The FOAM system has recently been transitioned to use the NEMO ocean model code (Madec 2008). This is a community model that has a wide user and developer base particularly in Europe. It is used for operational short-term and seasonal forecasting and climate modelling. It will form the ocean model component of the Met Office seasonal forecasting and climate modelling systems in the near future.

The model uses a linear free surface, and an energy- and enstrophy-conserving form of the momentum advection. 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 uses a combination of laplacian and bilaplacian operators, since this has been found to better represent features like the the Gulfstream separation at intermediate model resolutions (Chassignet and Garraffo 2001) .

The tracer equations use a TVD advection scheme (Zalesak 1979). The diffusion operator is laplacian and along-isopycnal. 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 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) (see also Delecluse and Madec 2000). 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.

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.

### Sea ice model

The sea ice component is currently modelled using the 2nd version of the Louvain-le-Neuve (LIM2) model (Fichefet and Morales Maqueda 1997). This has viscous-plastic dynamics (Hibler 1979) and a 3-layer thermodynamic model (Semtner 1976). This will be transitioned to use the Los Alamos CICE sea-ice model (http://oceans11.lanl.gov/trac/CICE) in spring 2012. This includes elastic-viscous-plastic dynamics and the possibility of using multi-layer thermodynamics and multiple ice thickness categories.

### 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. 2007). 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.

### Observation processing system

### References

Baumgartner, A. and E. Reichel, 1975 The world water balance. Mean annual global, continental and maritime precipitation, evaporation and run-off. 179 pp. Elsevier, Amsterdam.

Bell, M.J., 1994 Results from initial experiments with the assimilation of thermal profiles into a dynamical model of the Atlantic Ocean. Forecasting Research Division Technical Report Tech Rep 98. Available from Met Office, UK

Bell MJ, Forbes RM, and Hines A. 2000. "Assessment of the FOAM global data assimilation system for real-time operational ocean forecasting". J. Marine Sys., 25, 1-22

Bell MJ, Martin MJ, and Nichols NK. 2004. "Assimilation of data into an ocean model with systematic errors near the equator". Q.J.R. Meteorol. Soc. 130, 873-893

Chassignet, E.P. and Garraffo, Z.D., 2001, "Viscosity parameterization and the Gulf Stream separation". In "From Stirring to Mixing in a Stratified Ocean". Proceedings 'Aha Huliko'a Hawaiian Winter Workshop. U. of Hawaii. January 15-19, 2001. P. Muller and D. Henderson, Eds., 37-41

Cooper, M, and Haines, K. 1996. "Altimetric assimilation with water property conservation." J. Geophys. Res. 101(C1): 1059-1077

Delecluse, P. and G. Madec, 2000 : Ocean modelling and the role of the ocean in the

climate system. In Modeling the Earth’s Climate and its Variability, Les Houches, Session,

LXVII 1997, Eds. W. R. Holland, S. Joussaume and F. David, Elsevier Science,,

237–313.

Engerdahl, H. (1995), "Use of the flow relaxation scheme in a
three-dimensional baroclinic ocean model with realistic topography",
Tellus **47A** pp 365-382

Fichefet T, Morales Maqueda MA (1997) "Sensitivity of a global sea ice model to the treatment of ice thermodynamics and dynamics". J Geophys Res 102:12609–12646

Gaspar, P., Y. Gr´egoris, and J.-M. Lefevre, 1990 : A simple eddy kinetic energy model for

simulations of the oceanic vertical mixing Tests at station papa and long-term upper

ocean study site. J. Geophys. Res, 95(C9).

Hibler, W. D., 1979. "A dynamic thermodynamic sea ice model". Journal of Physical Oceanography, 9, 815 – 846.

Lorenc AC, Bell RS, and MacPherson B. 1991. "The Met Office analysis correction data assimilation scheme". Q.J.R. Meteorol. Soc. 117, 59-89

Madec G. 2008: "NEMO ocean engine". Note du Pole de modélisation, Institut Pierre-Simon Laplace (IPSL), France, No 27 ISSN No 1288-1619

Martin MJ, Hines A, and Bell MJ. 2007. "Data assimilation in the FOAM operational short-range ocean forecasting system: a description of the scheme and its impact." Q.J.R. Meterol. Soc. 133, 981-995

Semtner, A.J., Jr, 1976. "A model for the thermodynamic growth of sea ice in numerical investigations of climate". Journal of Physical Oceanography, 6, 379 – 389.

Zalesak, S. T., 1979 : Fully multidimensional flux corrected transport algorithms for

fluids. J. Comput. Phys., 31.

(Last Updated: 16-06-2011)