1230 Ocean Dynamics (2019) 69:1217–1237 Several studies (e.g. Shulman et al. 2013; While et al. 2010; Yu et al. 2018) applied the assimilation of physical observations so that in the BGC model only nutrients are updated, instead of all BGC model fields. We performed an alternative experiment in which the phytoplankton, zoo- plankton and detritus were excluded from the assimilation update. The assimilation influence on the RMSE and bias with regard to the in situ data is summarised in the right columns of Table 3. With this update variant, the RMSE of nitrate, chlorophyll, oxygen and silicate are reduced in both model grids by up to 2 % compared to the case when all fields are updated. However, the amount of bias increased in particular for oxygen and chlorophyll concentrations with increases of 6 % and 29 %, respectively. Note that here chlorophyll is particular because it is computed from the phytoplankton, which is not directly updated by the data assimilation in this experiment. In this experiment, the high concentrations in the Gulf of Finland were not present. 6 Assimilation using logarithmic concentrations Above, the strongly coupled assimilation was applied in the experiment STRONG-lin using the actual concentration values of the BGC fields in the state vector. As discussed in the introduction, chlorophyll concentrations can be well described as log-normally distributed (Campbell 1995) which motivated many assimilation studies to use the logarithm of the concentrations in the state vector. The analysis step in the Kalman filter assumes normal error distributions for optimality and taking the logarithm of a log-normally distributed field results in a normal distribution. Likewise, this transformation is then applied to other BGC variables. While using actual concentrations appears to be statistically inconsistent with the assumptions of the Kalman filter, the studies using actual concentrations in the assimilation were also successful. This can be mainly explained by the fact that the assimilation using actual concentrations still results in corrections of the correct sign. However, the size of the correction will be different because normal distribution is symmetric while the log-normal distribution is skewed. Using the logarithm will typically lead to a tendency to more strongly increase concentrations. According to our experience, using the logarithm also leads overall to larger changes to the concentrations and a more sensitive assimilation system in particular for non-observed parts of the model fields like below the ocean surface. Due to this, Pradhan et al. (2019) introduced a vertical localisation to stabilise the assimilation update of subsurface variables. In this vertical localisation, the assimilation increment computed for the full-water column is linearly reduced as a function of depth until it reaches zero at a prescribed depth (100 m in Pradhan et al. 2019). In Section 5.3, we found that the strongly coupled assim- ilation applied with the actual concentrations improved the oxygen concentrations, but the changes to the other BGC fields were very small. Here, the strongly coupled assim- ilation experiments of Section 5.3 are repeated using the logarithm of the BGC model fields (experiment STRONG- log) both with updating all fields of the BGC model and only updating the nutrients and oxygen. Using the logarithm of the concentrations in each ensemble state in the LESTKF, the cross-covariances used to update the BGC model fields are now computed from the logarithmic concentrations. In the experiment STRONG-log, unrealistic concentra- tions developed already during the second half of April. The experiments were stopped at the end of May. Table 4 shows very high RMSEs for the case that the assimilation is per- formed over the full water column (The columns labelled with ‘full vertical’ in Table 4). The behaviour was different in the North Sea from the Baltic Sea. While in the Baltic Sea extreme RMSEs occur for all BGC fields, the RMSEs remain in a reasonable range for chlorophyll and silicate in the North Sea. Here, mainly the north-eastern region along the Norwegian Trench was affected by unrealistically high concentrations (not shown). When the phytoplankton variables were excluded from the DA update (‘nutrients only’ in Table 4), the RMSEs were lower. However, in the Baltic Sea, the concentrations of most of the fields were still unrealistically high. In the North Sea, the silicate showed unrealistically high concentrations in the region of the Norwegian Trench while all other fields showed real- istic concentrations. This is in contrast to the case when all fields are updated which resulted in realistic silicate concentrations. When a vertical localisation is applied, the assimilation can be stabilised. With a localisation depth of 10 m, the concentrations in the North Sea become realistic if all BGC fields are updated and the RMSEs are similar to those of the FREE experiment (Table 4, compare columns 2 and 5). However, for the Baltic Sea this localisation is not sufficient and even with a vertical localisation depth of 5 m, the model fields show unrealistic concentrations. If only the nutrients are updated, only the nitrate concentrations in the Baltic Sea show unrealistic values in the Gulf of Finland and to a lesser extent in the southern Baltic Sea with vertical localisation. The unrealistic concentrations are not directly obvious from the value sof all RMSEs since the unrealistic concentrations can be very localised, e.g. in the eastern Gulf of Finland. Accordingly, they remain undetected if there is no in situ data available at this location. This case is exemplified for surface chlorophyll in Fig. 9. Here, the experiment WEAK (top left) results in concentrations of up to about 9 mg/m3 in the Baltic Sea. In the experiment, STRONG-log without