Adjustments of the control variables

Unique to our optimization is that corrections to the control variables are the only means for adjusting the model to reduce the model-data misfit while leaving the model dynamics untouched. Figure 12a shows the resulting normalized adjustments of atmospheric states averaged over the model domain. Changes of the atmospheric state in the first 4-year period are smaller than in the remaining years, which is caused by a low number of iterations in this chunk and the additional option to adjust the initial state in the year 2007. Because more iterations have been performed, corrections to the atmospheric forcing are more pronounced than those shown in the study of Koldunov et al. (2017).
Among all atmospheric states, wind components are adjusted most noticeably by the optimization algorithm. The 2-m air temperature and specific humidity are also substantially changed; still, their adjustments are smaller than those of the wind.  During the winter season, wind components seem to be the most efficient control variables because the Arctic Ocean is covered by sea ice blocking the heat and freshwater fluxes between the ocean and atmosphere. Although the same applies to the transfer of momentum, the free drift approximation in the adjoint enables the transfer of corrections to the wind, which is likely to be much less efficient than what the adjoint predicts. From April to October, the role of 2-m air temperature and specific humidity increase due to more open water.
We focus on corrections of the wind vectors in May (Figure 12b, c) and in November (Figure 12e, f) when the corrections are at the maximum and minimum, respectively. Normalized root mean squares of u and v wind correction anomalies depict substantial adjustments of wind vectors over seasonal sea ice extent regions in May (Figure 12b, c) and along the East Greenland Current (Figure 12e, f). Wind vectors in May are one of the most crucial factors that impact SIC in September (Kauker et al., 2009), indicating that wind vectors likely impact the SIC several months later thought sea ice advective convergence effects. Therefore, corrections to wind vectors in May and November may change SIC over the seasonal sea ice extent region months later.