Ocean Dynamics (2019) 69:1217–1237 1231 Table 4 RMS error 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 STRONG-log with logarithmic concentrations for the period April-May 2012 North Sea Field FREE STRONG-log STRONG-log STRONG-log STRONG-log Full BGC Full BGC Nutrients only Nutrients only Full vertical vloc = 10 m Full vertical vloc = 10 m Ammonium 0.98 63.31 0.98 0.97 0.97 Nitrate 13.35 1024.2 13.34 58.5 16.12 Phosphate 0.43 27.52 0.43 0.43 0.43 Chlorophyll 8.81 9.26 8.80 8.76 8.78 Oxygen 37.548 11497.1 37.559 37.56 36.56 Silicate 11.66 12.09 12.05 46.42 15.95 Baltic Sea Ammonium 1.30 5890.2 1499.1 7.99 1.29 Nitrate 12.58 6934.2 88.3 2702.2 15.21 Phosphate 0.251 3804.3 646.7 0.25 0.26 Chlorophyll 10.54 621.55 10.56 10.57 10.57 Oxygen 21.785 52183.8 21.166 23.01 21.13 Silicate 15.22 1833.8 15.18 17.06 15.18 Shown are separate values for the North Sea and the Baltic Sea. Shown are the experiments in which all fields of the BGC model are updated ‘full BGC’ and where only nutrients and oxygen are update ‘nutrients only’. The columns marked ‘full vertical’ refer to the assimilation without vertical localisation, while ‘vloc = 10 m’ refers a to vertical localisation of 10 m. The units are the same as in Table 2. The values in italic font indicate fields with unrealistic patterns vertical localisation and update of all BGC fields (bottom left), high concentrations of chlorophyll appear in the Gulf of Bothnia and the Gulf of Finland. In particular, the isolated regions of high concentration at about 20? E, 62.5? N (with concentrations up to 100 mg/m3) and in the Gulf of Finland (with concentrations up to 22000 mg/m3) are unrealistic. The same holds for the isolated regions of near- zero concentration (e.g. at the western end of the Gulf of Finland). With a vertical localisation of 5 m, the spurious high and low concentrations disappear everywhere except in the eastern Gulf of Finland, where still spuriously high concentrations exist. As there is no in situ data available at this location, this issue is not detectable from the validation with the in situ data. In contrast, in the North Sea, the chlorophyll field from WEAK and the two experiments STRONG-log updating all BGC variables with and without vertical localisation show only small differences and no unrealistic values. 7 Discussion The assimilation of SST data into a coupled ocean-BGC model has two aspects: the effect on the physical state and the effect on the BGC model. For the physical component, the SST assimilation showed improvements of the SST when compared to independent in situ data. Changes to the salinity were small, but actually, no strong error correlation between SST and salinity is expected. This also holds for the velocity field, which was not further discussed above. While at a single analysis state the horizontal velocities were influenced, their overall change was small and the velocities in the North Sea are strongly influenced by tides. The assimilation also influences the model state below the surface. For example, the strong temperature increases east of O¨land and Gotland shown for the surface in Fig. 5 also occur in lower model layers. Thus, consistent with earlier studies (Losa et al. 2012, 2014; Liu and Fu 2018), the full 3-dimensional physical model state was updated by the data assimilation and effects like the upwelling in July can be corrected. Nonetheless, the SST data cannot fully constrain the model and the assimilation of further observations like for sea surface salinity, sea surface height and velocities (like from HF radar observations, see, e.g. Barth et al. 2010) will be required. Further, the assimilation of subsurface in situ data will be required to further improve the lower layers for which surface data alone is not sufficient. For example, in the Danish straits, dense water of high density can flow from the North Sea into the Baltic Sea close to the bottom, which will not be detected by surface observations (see Losa et al. 2012, 2014, for discussions on this issue). For the effect on the BGC model state, different cases exist. For the weakly coupled case in which the BGC model fields react only dynamically to the changed physical state, the experiments show only small changes. In the validation with independent in situ data only, the oxygen