Ocean Dynamics (2019) 69:1217–1237 1225 Further, through the covariances estimated by the ensemble, the observational information is interpolated spatially and unobserved model fields are modified. For the coarse grid (upper panel), the RMSE of the forecast and analysis is clearly reduced compared to the free run. For the fine grid (lower panel), the RMSE is also reduced, but the fluctuations of the errors between the different analysis times are larger and the overall error reduction is smaller. Namely, the average RMSE is reduced in the forecast by 0.21 ?C (from 1.02 ?C for the free run to 0.81 ?C) on the coarse grid while the reduction is 0.14 ?C (from 0.89 ?C to 0.75 ?C) on the fine grid. Nonetheless, on the fine grid, the error is lower on average compared to the coarse grid. The strong variations of the RMSE, which are particularly visible for the fine model grid, are mainly due to the varying data coverage in between the analysis times. Both the number of observations and the observation locations varied strongly, so that the computation of the RMSE covers different regions and a strongly varying number of comparison points, which leads to sampling errors. For example, on the 10th of May at 12 h, when the highest RMSE occurs on the fine grid, only 893 grid points out of 124,000 overall surface grid points were observed. Just before, at 0 h on the 10th of May, there were 12275 observed grid points and at 0 h on the 11th of May, 2464 observations were available. Likewise on the 11th of May at 0 h, there is a very low number of only about 2000 observed grid points in the coarse grid and a particularly small RMSE. Apart from this effect, the data assimilation process of alternating analyses and forecasts induces a gradual modification of the ocean state over time as is visible from the small difference between the RMSE in the forecasts and analyses, but larger RMSE in the free run. Accordingly, the RMSE of the forecast or analysis at a certain time, depends on the observations that have been assimilated before. Overall, the variability of the RMSE is mainly caused by the coverage of the observations and less by specific oceanographic events. While the spatially averaged RMSE of the forecasts shows only small reductions by the data assimilation up to 0.21 ?C (and 0.24 ?C for the analysis states), the assimilation influence is locally much larger. Figure 5 shows the effect of the assimilation as an average over July 2012. The RMSE in the FREE run (upper row) is mainly below 0.8 ?C in both grids, but it is larger in the western side of the English channel, in the region of the Norwegian trench, along the south-eastern coast of Sweden, the Gulf of Bothnia and at the southern coast of Finland (see Fig. 1 for geographic information). Locally, the RMSE exceeds 4 ?C. The data assimilation strongly reduces these high errors almost everywhere except in the far northern end of the Baltic Sea and in the English channel (middle row). In the fine grid, the error reductions are particularly visible at the southern coast of Sweden and along the German coast of the Baltic Sea. The bottom row of Fig. 5 shows the actual change in the temperature. In most regions of the model domain, the assimilation has reduced the temperature. However, east of the islands O¨land and Gotland, the temperature is increased up to 2 ?C. Here, upwelling of cold water was present in the free- model run, which is not present in the observations. The assimilation of the SST data increases the SST in the full- water column, hence decreasing the RMSE. Overall, the error reductions are similar to those described by Losa et al. (2012, 2014), where SST data with a similar model was used without a refined nested grid. The comparison with the assimilated observations shows that the assimilation system is successful in incorporating the observational SST data. Table 1 shows the RMSEs computed with regard to the in situ observations of SST over the full period from April to July 2012. The number of in situ data is overall low with Table 1 RMS error and bias with regard to in situ data for both model grids for the FREE run and the forecast and analysis from the experiment WEAK for the period April to July 2012 Surface temperature ( ?C) RMSE Bias Grid No. points Free Forecast Analysis Free Forecast Analysis Coarse 6674 1.070 0.925 0.920 0.482 0.300 0.297 Fine 800 1.151 1.053 1.052 0.424 0.247 0.246 Surface salinity (psu) Grid No. points Free Forecast Analysis Free Forecast Analysis Coarse 6472 1.430 1.387 1.385 ? 0.266 ? 0.222 ? 0.217 Fine 796 2.763 2.770 2.773 0.732 0.617 0.617 The upper rows show the errors and bias for SST in ?C, the lower for surface salinity. The second column shows the number of collocation points