This work describes two improvements to the assimilation of satellite sea surface temperature (SST) retrievals into a regional ocean model. The first is a bias correction scheme to make SST data from multiple providers more consistent before they are assimilated. The second improvement is an observation operator for passive microwave SST that correctly accounts for the difference in resolution between the measured and modelled SST. 

The manuscript is well structured and results and methods are clearly explained.

I have only a few comments/suggestions:

L91: Could you elaborate on why the observational error is constructed to be dependent on the model background error in this way? I didn't find how the background error covariance B is modelled, but I imagine it has a very different spatial structure than the satellite SST error.

Sec. 2.2: I think it would be good to include a discussion on how IR sensors intrinsically measure the skin temperature and how their measurements are converted to sub-skin temperature for the different products. For most products this is done by the data creator, but for Sentinel-3A the conversion is done by the authors by adding a constant offset of 0.17°C. Since Sentinel-3A is subsequently used as the reference satellite, this simple offset could possibly degrade measurements from satellites that use more sophisticated solutions.

Tab. 3: Is it possible to include the metrics for the free model run in this table? The fact that PWM2 is similar to the free model in terms of spectrum (L330) makes me curious to see how much the impact of assimilating with the supermod operator really is.

L263: Are the reduced increments for PMW2 compared to PMW1 not simply a result of the choice of the parameter alpha?

L270: Is the fact that PMW SST fills in the gaps of IR SST sufficiently represented in the performance of the combined experiments? If the comparison with satellites is using IR SST, it does not take into account situations where only PMW SST is available and you may be underestimating the performance.

The paper “Improving the SST in a regional ocean model through refined SST

Assimilation” describes a new system to assimilate passive microwave data into a regional model near Norway.  The bias correction system for these data and a new observation operator (the supermod operator) are described.  The authors claim improved results from these new systems giving statistics from a run coving April-June 2018.  A spectral analysis is also presented.

A full list of my comments can be seen in the attached marked up PDF

In general I found the paper to be well written and the figures to be of good quality.  Aside from some missing references, I am also happy with what is presented on the bias correction.

However, I found the supemod part of the paper to be much less convincing and I think this needs considerable work. I have a number of problems with this work:

• The authors have reduced the observation error variance when supermodding by a factor of more than six. While some change in observation error would be expected, no proper argument is given for the values chosen.  From their results I think it is possible that this was too large a reduction and the authors are overfitting the data. Also, I would have expected to see an additional experimental run where the observation errors have not been changed so the effect of the supermod operator could have been seen in isolation.
• The results shown indicate an increase in power in the high wavenumbers in the model. However, I don’t understand this as the increments are visually smoother (figure 7).  This needs to be properly explained. Also, the power spectrum of the increments, not just the model, should be given.
• The supermoded observations resulted in significantly degraded statistics. I found the authors assertion that this was due to a “double penalty” issue to be unconvincing. This is because neither the resolution of the model nor the verification data has changed. It’s also because the increments look smoother to me (see above bullit point).  I think it is more likely that they are overfitting the data and putting noise into the model.  The authors either need to provide much better evidence to support their beliefs and refute mine, or they need to recalibrate the assimilation to reduce overfitting.

These are major issues with the manuscript and will require work to resolve.  However, I believe the paper is of interest and that the problems can be addressed.  Therefore I am recommending the manuscript for major revision.