A nested-grid model with data assimilation in the Gulf of Lions

When a model combines the use of nested grids and data assimilation, a preliminary, simple, 1D test case showed the interest of combining the different state vectors coming from the different grids, into one single vector, and using global error matrices covering all the grids at once. In this case, the assimilation procedure provides errorspace feedback from the fine grid to the coarser grid, which proves to be even more important than the statevector feedback. For data located in the fine grid, assimilation of the same data in the coarse grids is not necessary anymore, as both model and errorspace feedback is performed during assimilation. Large data transfers from local to basin-scale models can be avoided.
The GHER hydrodynamic model (for a full description, see e.g. [1]) is applied to a three times nested model covering (a) the Mediterrannean Sea at 1/4 degree, (b) the Liguro-Provencal Bassin at 1/20 degree, and (c) the Gulf of Lions at 1/100 degree.
The simulation starts on Januari 1st, 1998, using ECMWF atmospheric forcings and MODB4/MEDAR climatic data. As the model allows mode splitting, the simulation uses 2D timesteps of 3 seconds, and 3D timesteps of 3 minutes, on each grid.
A twin experiment is performed. The perturbed initial condition is a delayed model state of the reference run. An initial reduced-rank model errorspace is constructed from 20 EOFs, themselves built from the reference run, over all three grids at the same time. Surface temperature and salinity from the reference run are assimilated in the model every 24 hours, using reduced-rank optimal interpolation (see [2]). Different simulations are implemented, using different ways to combine grid nesting and data assimilation: with or without state vector feedback, with data assimilation only in the local grid, or in the coarser grids, or both, and with or without errorspace feedback (i.e. with 3 separated statevectors or with one global statevector). The comparison of those experiments comfirms that using one global statevector reduces the error in the coarser grids much faster.
The effect of data assimilation, and the performances of the different methods, can be examined by calculating RMS errors between the perturbed runs and the reference run. They can also be observed by following the model state trajectory in the EOFspace (for example, using the first three EOFs). In the context of the twin experiment described above, the first assimilation cycle clearly brings the model back in time. This is consistent with the choice of the perturbed initial conditions, being a delayed state of the reference run. The following assimilation cycles have little effect, as the trajectory is already almost brought back on the reference trajectory. If other parameters are modified too (e.g. the atmospheric fluxes), each assimilation cycle has an important effect on the modelstate trajectory.
A new experiment performs assimilation in the Gulf of Lions in the spring of 1998 using real observations. Different variables can be assimilated, using data collected during the FETCH campaign: NOAA/AVHRR SST, temperature and salinity from Atalante CTDs, or altimetric data from the ERS2 or TOPEX satellites.