The TOPAZ4 and PIOMAS reanalyses

Available variables from the TOPAZ4 (Xie et al., 2017) and the PIOMAS (Lindsay & Zhang, 2006) reanalyses are compared with our reanalysis. Table 2 lists the details of the two reanalyses. The three systems show significant differences. The PIOMAS reanalysis assimilates the least observations and the coarsest resolution among the three products. The data assimilation methods in the TOPAZ4 and our reanalysis are computational more expensive than the PIOMAS reanalysis and more observations are assimilated. 

Evaluation of the optimization

The optimization involved running the MITgcm forward to evaluate the cost function over the time frame 2007-2016, split into three sections as described above. The adjoint model integration then provided gradients of the cost function with respect to control parameters, which were used in an iterative way to minimize the model-data misfit. In the end, a total number of 15, 21, 20 iterations were performed in the three chunks, respectively. Figure 2 shows the resulting percentage decrease in the total cost function and the individual cost components in the three chunks. Negative values indicate that the model-data misfits are increased for that type of observation. The total cost reduction is more than 30% in the three fragments. SST, SIC, and climatological temperature (WOA-T) and salinity (WOA-S) dominate the total cost function (magenta bars) and are reduced by 40%-60%. For the other constituents, MDT and SIT, errors are reduced by more than 50%, but SLA and SIC-SST are degraded. Compared to Koldunov et al. (2017), the present optimization achieves a larger cost function reduction for the total and individual components. Besides starting from a better first-guess solution, the increased cost function reduction, in particular, results from the larger number of iterations performed here. We note that the cost constituents of temperature and salinity profiles establish ~20% and ~10% of the total cost, respectively, and that the optimization is not capable of reducing those misfits significantly.
Because they appear as the largest improvement during the optimization, in the following section, we focus on the improvements of SIC, SIT, and SST. We compare resulting fields with those available from the TOPAZ4 (Xie et al., 2017) and the PIOMAS (Lindsay & Zhang, 2006) reanalyses. We also examine the impacts of data assimilation on oceanic transports and freshwater content and compare these variables against the TOPAZ4 reanalysis.