Impact of changing the assimilation cycle: centered vs staggered, snapshot vs monthly averaged

In NorCPM runs we currently assimilate data every month centered (in the middle of the month) and we correct the instantaneous restart file based on the monthly averaged of that month. It implies that we compare monthly average observations with instantaneous model snapshot. This approach is compared to shifting the assimilation at the end of the month (assimilating past monthly observations) and comparing monthly average observation with model monthly average. Also, one corrects the initial condition at the start of the hindcast instead of 15 days earlier. For reanalysis, assimilating data in the middle of the month outperforms the scheme where data is assimilated at the end of the month. No significant difference is found between the two schemes for seasonal prediction skill.