Ocean Dynamics (2019) 69:1217–1237 1223
concentrations of the BGC variables. In this case, the
statistical update computed by the LESTKF can result in
negative concentrations. As in Yu et al. (2018), these values
were reset to zero but occurred only in a few cases in the
experiments. The experiment STRONG-log performs the
assimilation using the logarithm of the concentrations.
The experiments allow us to assess whether the cross-
covariances between SST and BGC model fields are
sufficiently well estimated to result in an improvement of
the BGC fields. For this, the root mean square error (RMSE)
and the mean error (bias) between the state estimate from
each data assimilation experiment with regard to the in situ
validation data are computed. To assess the impact of the
SST data on the modelled surface temperature and salinity
we also compute the RMSE with regard to the assimilated
data as well as RMSE and bias with regard to independent
in situ data of temperature and salinity.
5 Results
To analyse the assimilation results, first the influence on
the surface temperature and salinity are assessed. Then,
the effect of the weakly coupled assimilation on the
biogeochemical model fields is examined, and finally, the
effect of the strongly coupled assimilation is assessed.
5.1 In?uence of the assimilation on surface
temperature and salinity
The effect of assimilating satellite SST data on the physical
ocean state was already discussed by Losa et al. (2012,
2014), so no detailed analysis is performed here. Figure 4
shows the RMSE with regard to the assimilated SST
observations for the analysis and forecast fields each 12 h
as a time series for both model grids. For the forecasts, the
RMSE is computed with observations that have not yet been
assimilated. Given that the coverage of the SST observations
varies in between the analysis times, the observations at
the forecast time are partly independent, while they are
not independent for the analysis. Nonetheless, the values of
the RMSE for the forecast and analysis are very similar.
Since HBM-ERGOM uses a one-way coupling between
the physical and biogeochemical models, the physical
model fields are identical in the experiments WEAK and
STRONG. The assimilation of SST data pulls the SST in
the model toward the observations while accounting for the
uncertainty in both the model state and the observations.
Fig. 4 RMS error with regard to the assimilated SST observations over
time. The upper panel shows the RMSE for the coarse model grid while
the lower panel shows the fine grid. The lines are (green) the RMSE
for the free model run, (black) the values directly after the analysis step
and (blue) the RMSE for the 12-h forecasts
