Twelve monthly experiments of 4D-variational assimilation in the tropical Atlantic during 1987: Part 1: Method and statistical results

Abstract

GEOSAT sea level anomalies, XBT temperature profiles and Levitus (1982) climatologies are assimilated monthly during 1987 into a non-linear primitive equation model of the tropical Atlantic ocean. The model has a resolution of 1° longitude × 1/3° latitude × 20 vertical levels extending from 50°S to 50°N. The model physics are complex, including in particular an imbedded 1D-mixed layer model and a 3D-Richardson number dependent mixing under the mixed layer. The model is forced monthly by ship winds and Oberhüber (1988) climatologies of heat and fresh water fluxes. A 2° longitude × 1° latitude gridded optimal interpolation analysis of GEOSAT sea level anomalies is assimilated between 20°S and 20°N at each grid point of the model. Validated TOGA XBT profiles are also assimilated between 30°S and 30°N at their exact location. Decorrelation in space and time is assumed for the error structures. Data weights are taken to vary with data accuracy and with a proxy function of the model representativity. The variational assimilation succeeds in determining initial conditions that reduce the model-data misfits and demonstrates that the temperature and the sea surface height of a general circulation model are sensitive to initial conditions. Despite the complex evolution of the present model over one month, the adjoint model is able to provide efficient descent directions for the minimization algorithm. Thus, 4D-variational assimilation can be used in the tropics with a general circulation model. The assimilation of satellite altimetry helps to reduce the misfit between the model and the XBT profiles. The decay of the XBT misfit is faster and the corrections are not localized to the XBT positions but influence the whole basin. The biggest impact appears where the GEOSAT variability is the highest, e.g. around the North Equatorial Counter Current and the North Equatorial Current (5°N–15°N). The assimilated sea level variability is close to the GEOSAT variability. On the other hand, the spatial variability of the modelled temperatures is less well defined in comparison with the XBT profiles; although the large scale is reproduced, details are missing in the vertical stratification at the surface and in the thermocline. The modelled equatorial upwelling is also too strong after assimilation with a 2°C cold bias at the surface in July. The 11 one-month forecasts in 1987 following each month of assimilation show an improvement of the simulation with reference to XBT profiles below the mixed layer. Temperature profiles in the mixed layer are neither improved nor degraded. This could indicate the need of a better time resolution of the forcings, for example including the diurnal cycle and a prognostic model of the mixed layer. Compared to GEOSAT, the forecasts of 1987 show an improvement up until May. The equatorial upwelling of July is degraded by the assimilation, because of a combination of the heat flux correction and the surface cold bias which is increased by the assimilation. This demonstrates that the inadequacy between the heat fluxes and the mixed layer model is a critical issue with assimilation in thermodynamical models. The pure forecast over the first 7 months of 1988 compares well to XBT profiles under the thermocline, showing that the initialization of the model has a positive impact for more than 7 months. The description of the warm anomaly of early 1988 relative to 1987 is globally improved by the assimilation. In particular, the variability of the north equatorial currents measured by altimetry is only reproduced after data assimilation. There is a benefit for the year-to-year signal in the Gulf of Guinea. This emphasizes the importance of the in situ observing network and satellite altimetric data.