High latitude nudging: hmean nudging
In MUSOC model, we also include the column-wise nudging, extending to the entire layer at the high latitude with annual climatological state. This gives internal effective heat and salt material "sources" not in the real ocean. However, this should give model climatology close to the real ocean with the "sources" magnitudes being a metric of model quality; they should decrease with increased resolution and better model physics and subgridscale mixing emulation.
The formulation in musoc
Currently, we add this nudging term at the last iteration step regarding filtered-leap frog scheme, which are the `T_2` and `S_2` variables in the model. Even though the nudging apply to the entire water column, for surface layer, we nudge towards the current month state:
`T_2(\:,:,2:k1)=(1-h_{str})*T_2(\:,:,2:k1)+h_{str}*T_{an\n"_"cli}(\:,:,2:k1)`
`S_2(\:,:,2:k1)=(1-h_{str})*S_2(\:,:,2:k1)+h_{str}*S_{an\n"_"cli}(\:,:,2:k1)`
`h_{str}=1/(tau*daodt)`
here,`tau` is the time scale for nudging, `h_{str}` is the nudging strength and `daodt` means the number of timesteps per day. Notes that `T_{an\n"_"cli}` means the "annual" mean of the climatology. For the surface layer salinity, we use current month climatology state and times the mask at lower layer. This approach aims to prevent the coastal region response due to the limited depth:
`S_2(\:,:,1)=S_2(\:,:,1)+ h_{str}*mask(\:,:,1)*mask(\:,:,2)*(S_{cli}(\:,:,1)-S_2(\:,:,1))`