This means that the ocean data assimilation system must provide the full ocean state, not simply the anomaly. Other coupled models normally make some other approximations, for example, Ji et al. (1996) only couple anomalies about the mean model state.
This paper discusses the sensitivity of the ENSO forecasts to the ocean initial conditions. In particular the importance of assimilating sub-surface ocean observations, for example, from the TOGA-TAO (Tropical Atmosphere Ocean) array, is explored. Also investigated is the sensitivity of the forecasts to initial conditions provided by assimilating the same sub-surface data but using different wind forcing during the assimilation integration. This leads to some possible insights into the sensitivity of the forecasts to errors in the initial state.
MODELS AND ASSIMILATION SCHEME
Ocean model
The ocean model used is based on HOPE (Hamburg Ocean Primitive Equation model) version 2 (Latif et al. 1994, Wolff et al. 1997). The main differences to this basic version are: the horizontal pressure gradients are calculated at the middle rather than the bottom of each model layer (this allows the sea level gradients to be more consistent with the pressure gradient field and has been found to be important for sea level assimilation), the use of a pseudo ice model to constrain the model solution over the polar regions and a slightly different topography. The model is global and with 20 vertical levels. Horizontal discretisation is on an Arakawa E grid with a variable grid spacing: the zonal resolution is 2.8°and the meridional resolution varies from 0.5° in the equatorial region (within 10 degrees of the equator), smoothly increasing to 2.8° in the mid-latitudes (from 30 degrees polewards).
The model is forced at the surface with specified fluxes of heat, momentum and fresh water. The solar radiation penetrates below the surface layer exponentially. When the ocean model is run to produced initial conditions (with or without data assimilation, but not coupled forecasts), additional relaxation terms for temperature and salt are used to constrain these fields at the surface to prescribed fields as described later.
Ocean data assimilation system
An ocean data assimilation scheme is used to introduce sub-surface observations into the ocean model. It is based on the statistical interpolation scheme described by Smith et al. (1991). This is essentially an optimum interpolation carried out on overlapping sub-domains of the model horizontal grid. Where domains overlap the analyses are smoothed together. The breakdown of the globe into sub-domains depends on the observation distribution and is done so that the maximum number of observations within the domain is less than 200. This is so as to reduce the cost of matrix inversion, see Smith et al. for full details. The optimum equations are solved for each level of the model independently, only over the top 1000m. There is no assimilation in the top model level, instead it is relaxed to the Reynolds (1988) observed SST with a relaxation time scale of 3 days.
The model background errors are represented by gaussian functions which are anisotropic and inhomogeneous. The values follow Smith et al. (1991). Within 4 degrees of the equator the correlation length scale in the E/W direction is 1500km while in the N/S direction it is 200km. In the sub-tropics and high latitudes, polewards of 15 degrees, the correlation length scale is 400km in all directions. Between the equatorial strip and the sub-tropics there is a smooth transition in correlation scales. Observation errors are assumed to be correlated in space and time, with a spacial correlation function with length scale of 2 degrees and a time correlation scale of 3 days.
