1226 Ocean Dynamics (2019) 69:1217–1237 6674 points on the coarse grid and 800 points on the fine grid. On the coarse grid, the assimilation reduces the RMSE from 1.07 ?C in the FREE run to 0.92 ?C in the analysis. The forecast RMSE is only slightly larger with 0.925 ?C. The RMSE of the FREE run is 1.15 ?C on the fine grid and hence larger than on the coarse grid. This is in contrast to the RMSE with regard to the assimilated satellite observations, where the RMSE on the fine grid is lower than on the coarse grid. The RMSE is reduced by the data assimilation to 1.05 ?C. Overall, the reduction of the RMSE is lower for the in situ data than the assimilated SST observations. The assimilation also reduces the warm bias of the model SST in both model grids. On the coarse grid, the bias is reduced by 62 %, while it is reduced by 58 % on the fine grid. So, the reduction of the bias is overall larger than that of the RMSE. The lower part of Table 1 shows the RMSE for surface salinity. Overall, the changes to the salinity RMSE are very small. The changes are due to the direct update of the salinity field through the cross-covariances between the temperature and salinity, but also due to the fact that the assimilation also influences the velocities. The assimilation reduces the error on the coarse grid from 1.43 to 1.39 PSU in the analysis. On the fine grid, the RMSE of the salinity is slightly increased by about 0.4 % by the assimilation. While the changes in the RMSE and bias are statistically significant for the coarse grid, only the change in bias is significant for the fine grid (at 95 % probability according to a paired t test). Locally, the largest changes happen in the transition zone between the salty North Sea (around 35 PSU) and the fresh Baltic Sea (5 to 8 PSU), i.e. the Danish Straits in the fine grid and the Skagerrak and Kattegat in the coarse grid. The assimilation also reduces the amount of bias by about 8 %. The model underestimates the salinity in the coarse grid, while it overestimates the salinity in the fine grid. 5.2Weakly coupled assimilation effect on the biogeochemical model ?elds In the weakly coupled data assimilation, only the physical model fields are directly updated by the LESTKF in the analysis step. The BGC model fields then react dynamically on the changed physical conditions during the following forecast phase. Table 2 shows the RMSE and bias computed with regard to the in situ data for 6 BGC variables. The changes are largest for oxygen with a reduction of the RMSE by 3.5 % and bias by 17 % on the coarse grid and a reduction of the bias by 64% on the fine grid. These changes are statistically significant at 95 % probability using a paired t test. Changes to other variables are generally smaller. To get more insight into the changes to the biogeo- chemistry which are induced by the data assimilation, we examine the surface oxygen during the month of May 2012. Figure 6 shows a monthly averaged oxygen concentration Table 2 RMS error and bias of biogeochemical fields with regard to in situ data at the surface for both model grids and the FREE run and forecast and analysis from the experiment WEAK for the period April to July 2012 RMSE Coarse grid Fine grid Field Free Analysis No. points Free Analysis No. points Ammonium 1.562 1.561 1146 1.393 1.394 228 Nitrate 11.116 10.810 1372 12.914 13.118 366 Phosphate 0.421 0.421 1392 0.303 0.299 366 Chlorophyll 8.203 8.205 1428 5.781 5.783 306 Oxygen 39.595 38.195 1494 34.297 34.800 426 Silicate 17.979 18.092 1188 8.361 8.404 366 Bias Field Free Analysis No. points Free Analysis No. points Ammonium ? 0.428 ? 0.430 1146 ? 0.643 ? 0.643 228 Nitrate 3.154 3.071 1372 3.760 3.622 366 Phosphate 0.035 0.033 1392 0.083 0.078 366 Chlorophyll ? 2.208 ? 2.207 1428 ? 1.34 ? 1.325 306 Oxygen ? 17.030 ? 14.192 1494 ? 3.117 ? 1.114 426 Silicate 3.040 3.038 1188 ?3.343 ? 3.404 366 Shown is also the number of collocation points. The units are mmol N/m3 for ammonium and nitrate, mmol P/m3 for phosphate, mmol O/m3 for oxygen, mmol Si/m3 for silicate and mg Chl/m3 for chlorophyll