Ocean Dynamics (2019) 69:1217–1237 1233 LESTKF, like any ensemble Kalman filter, perform a linear regression between the observed and unobserved model fields or locations (see, e.g. Anderson 2003). While the linear relationship will always hold for small errors (in the sense that a Taylor expansion could be truncated to the linear term), large errors will result in nonlinear relationships. This is also expected for the nonlinear processes of a BGC model as was, e.g. discussed for the assimilation of satellite data on phytoplankton functional groups by Ciavatta et al. (2018). Perhaps, the errors in the BGC model state are here too large for the linear assumption. Overall, the corrections in our real-world application are smaller than those obtained in the idealised twin experiments performed by Yu et al. (2018). The question whether BGC fields should be treated in the assimilation with their actual concentrations or with the logarithm of the concentrations is still open. In experiments using 3D variational assimilation, Teruzzi et al. (2014) found for chlorophyll that vertical covariances constructed using empirical orthogonal functions were less represen- tative when logarithmic instead of actual concentrations were used. However, at least for chlorophyll the model of a log-normal concentration distribution was established (Campbell 1995) and the dynamically generated ensemble used here should be able to represent the vertical covari- ances. For other variables than chlorophyll, the distribution is less clear. The distribution of oxygen in Fig. 7 shows only a small range and does not appear to be log-normally dis- tributed. Even more, the assimilation bases on the assumption that the error distribution is normal and the distribution of the errors does not need to follow the distribution of the field itself. Basing on this open discussion, the com- parison of the experiments STRONG-lin and STRONG-log shows the different effects of applying the assimilation to the actual concentrations or to their logarithm. In particu- lar, STRONG-log leads to unrealistic concentrations. The positive influence of the vertical localisation shows that the linear regression of the surface temperature increments onto logarithmic subsurface concentrations leads to unrealistic values. These unrealistic concentrations then influence also the surface through the model dynamics. However, unreal- istic concentrations can even happen directly at the surface as the following example shows. To get more insight into the development of the unrealistic concentrations, we examine the profiles of chlorophyll concentration at different dates at two locations where extremely high concentrations are visible in Fig. 9: in the Gulf of Bothnia at 19.79? E, 62.73? N and in the Gulf of Finland at 27.54? E, 60.33? N (see Fig. 1 for the locations). The left panel of Fig. 10 shows the chlorophyll concentration in the Gulf of Bothnia. The profile looks still realistic on the 22nd of April. However, a deep maximum develops from the 23rd of April around 40 m of depth. This maximum continues to grow to extreme values and, due to the model dynamics, also leads to an unrealistic concentration increase towards the ocean surface. The chlorophyll concentration is computed from the concentration of the three phytoplankton groups of ERGOM. Of these, the diatoms and the flagellates show unrealistically high subsurface concentrations, while the concentration of cyanobacteria remains realistic. The largest increases to the concentrations at this location happen during the analysis step. This behaviour shows that in the course of the assimilation process, large cross- covariances developed between the SST and the subsurface concentrations of diatoms and flagellates, which lead to unrealistic assimilation updates in the linear regression. Fig. 10 Chlorophyll profiles at four dates in April at two locations where unrealistic concentrations develop: (left) in the Gulf of Bothnia, where first an unrealistic deep maximum develops; (right) in the Gulf of Finland, where the concentration increases over most of the water column