Hi Ming Chen!
I apologize for the delay in my response, however, I was able to get the GFS data to work, and I am able to get results similar to yours. The trick was to set the vertical levels of MPAS to only extend to 28000 meters, rather than 30000.
However, our issue seems to be further from being fixed with the new snow height. I performed a series of simulations changing the snow height. The results can be seen in the attached plot. The black line represents the ERA5 data, the orange line represents an MPAS run with ERA5 default initial conditions, the blue line is an MPAS run with the snow height over sea ice fixed at 1 meter, the green line is an MPAS run with the snow height over sea ice fixed at 5 meters, and the two olive lines represent MPAS runs using GFS initial conditions. The solid olive line is using the default MPAS code, and the dashed olive line is using your fix for the initial conditions processing.
As you can see, the larger the snow height, the colder the skintemp, and MPAS is already biased cold as compared to ERA5. So while it is probably an issue that MPAS is not capturing the snow height correctly from ERA5 initial conditions, the issue of the cold bias remains and becomes worse when we fix the snow issue.
Additionally, as you can see from the plot attached here and from the SST anomaly plot I attached on the first post, the sea surface temperatures in MPAS under sea ice are well below freezing, which is unphysical. I have found some attempts in the model code to prevent the SST under sea ice from going below 271 K, but evidently these are not working correctly.
All of this is to say, there might be a larger issue here that needs addressing, which is how MPAS initializes the sea surface temperature underneath sea ice points. If that were to be repaired, this might fix the skin temperature issue, as I believe that the skintemp above sea ice is sensitive to the temperature of the ice below it, which is being set to unphysically cold levels via the sea surface temperature initialization issue.
Let me know what you think of this. If you have any thoughts on how to fix the sea surface temperature under sea ice issue, I would love to hear about it. Thank you for your continued help on this issue!
Calvin
EDIT: There seems to be an issue with file uploads on the forum currently. I will send you an email with the plot and post it here when this issue is resolved.