Weak constraint 4D-Var data assimilation in the Regional Ocean Modeling System (ROMS) using a saddle-point algorithm: Application to the California Current Circulation

The saddle-point formulation of weak constraint 4-dimensional variational (4D-Var) data assimilation has been developed for the Regional Ocean Modeling System (ROMS), and is applied here to the California Current System (CCS). Unlike the conventional primal and dual forcing formulation of weak constraint 4D-Var, the saddle-point formulation can be efficiently parallelized in time, leading to a substantial decrease in wall-clock run time. The performance of the ROMS saddle-point 4D-Var algorithm is assessed here and compared to that of the dual forcing formulation which is the current standard in ROMS. While the rate of convergence of the saddle-point formulation is slower than the dual forcing formulation, the increase in computational speed due to timeparallelization can more than compensate for the additional inner-loop iterations required by the saddle-point algorithm in the CCS configuration considered here. Further gains in performance can be achieved by running the 4D-Var inner-loop iterations at reduced resolution and/or reduced arithmetic precision. The results presented here indicate that in high performance computing environments with large numbers of available compute cores, the saddle-point formulation of 4D-Var could significantly reduce the run-time compared to the dual forcing formulation for large data assimilation problems.