Ocean Dynamics (2019) 69:1217–1237 1229 Table 3 RMS error and bias of biogeochemical fields of the data assimilation analysis state with regard to in situ data at the surface for both model grids from the experiment STRONG-lin for the period April to July 2012 Update Full BGC Nutrients only Coarse grid Fine grid Coarse grid Fine grid Field RMSE Bias RMSE Bias RMSE Bias RMSE Bias Ammonium 1.560 ? 0.419 1.402 ? 0.640 1.558 ? 0.430 1.394 ? 0.640 Nitrate 10.903 3.293 13.055 3.750 10.812 3.229 12.803 3.679 Phosphate 0.428 0.041 0.319 0.101 0.423 0.030 0.319 0.099 Chlorophyll 8.360 ? 1.71 5.830 ? 1.217 8.183 ? 2.204 5.800 ?1.298 Oxygen 37.731 ?12.911 34.964 ? 0.336 37.510 ? 13.704 34.820 ? 0.367 Silicate 18.246 3.508 8.339 ? 2.885 18.177 3.557 8.239 ? 2.785 Shown are the cases that all BGC variables are updated by the data assimilation (columns ‘full BGC’) and that the phytoplankton variables are excluded from the update (‘nutrients only’). The units are the same as in Table 2 the ensemble). In this section, the assimilation effect for the experiment STRONG-lin is examined, i.e. for the case that actual concentrations are used in the LESTKF. The experiment STRONG-log is discussed in Section 6. Table 3 shows the RMSE and bias with regard to the in situ data for the experiment STRONG-lin. The change in the RMSEs is slightly larger than for the weakly coupled assimilation. The largest change happens for oxygen on the coarse grid where the RMSE is reduced by 4.7 % in the experiment STRONG-lin, while it was only reduced by 3.5 % in WEAK. Further, the amount of bias is now reduced by 24 % compared to 17% in WEAK. On the fine grid, the amount of bias is also more strongly decreased (by 89 %), while the RMSE is now increased by 1.9 %. The changes to the other fields are still small. Noticeable is a reduction of the bias for chlorophyll on both grids and for silicate on the fine grid. The RMSE for chlorophyll was essentially unchanged in WEAK but is increased slightly in STRONG-lin. Actually, in the eastern Gulf of Finland the chlorophyll concentration was unrealistically high during the first half of May in STRONG-lin. This effect will be further discussed in Section 7. Further, the biases for nitrate and phosphate are increased in STRONG-lin in the coarse grid, while they were marginally decreased in WEAK. Figure 8 shows the change in the oxygen field averaged over May 2012. Compared to the weakly coupled assimilation, the strongly coupled assimilation results in larger changes up to 24 mmol/m3. Further, the strongly coupled assimilation leads to larger changes in the North Sea up to 10 mmol/m3. The bottom row of Fig. 7 shows the comparison between the model and in situ data for May 2012. The strongly coupled assimilation further increases concentrations that were above 340 mmol/m3 in the experiment FREE compared to the experiment WEAK, which reduces both RMSE and bias on both grids for this month. Fig. 8 Change in oxygen concentrations caused by the strongly coupled assimilation experiment STRONG-lin shown as the difference of the experiments STRONG-lin minus FREE. The strongly coupled assimilation leads to larger changes compared to weakly coupled assimilation