The inclusion of ice-shelf cavities and melt rates below ice shelves around Antarctica is a major objective of the E3SM Cryosphere Campaign. Sub-ice-shelf melt rates are needed in order to estimate future mass loss from the Antarctic Ice Sheet. Along with dynamic ocean boundaries, they are an important component in future coupling between MPAS-Ocean and MALI.
MPAS-Ocean implements the topography of ice-shelf cavities by allowing the sea-surface height (SSH) to follow the ice shelf-ocean interface (the ice draft). The sea surface is depressed by applying the pressure of the overlying ice shelf as a top boundary condition. The Vertical coordinate in ice-shelf cavities is a bit more complex than the simpler z* coordinate used elsewhere in the ocean domain because ocean layers have to be made thicker or their slope has to be reduced via smoothing to prevent the Haney number (Haney 1991) from becoming too large.
Sea surface height adjustment¶
Standalone-ocean test cases typically provide the ice draft (which is then used
ssh) rather than the pressure from the weight of the ice shelf
landIcePressure variable). This is in contrast to coupled
ice sheet-ocean configurations that we expect to support in the future, in
which the weight of the ice is know, rather than the ice draft. Ideally, the
initial ice draft and the ice-shelf pressure would be consistent with one
another, so that the SSH would remain nearly stationary in time once the
MPAS-Ocean simulation starts. In practice, this is difficult to achieve.
Typically, ice shelves are assumed to be freely floating on the ocean with negligible stresses, meaning that the ice draft and the weight of the ice are related through the average density of the ice and of the displaced ocean water in a given column. However, in most circumstances it is hard to accurately determine the average density of displaced ocean water, and details of the numerical algorithm for computing the horizontal pressure gradient can also affect how consistent the ice draft and pressure fields are.
MPAS-Ocean achieves a consistent ice draft and ice-shelf pressure by:
making an initial guess that the displaced ocean density is the same as the density in the top ocean layer and
iteratively performing short (typically 1-hour) forward simulations in which the SSH is free to evolve, then modifying the ice-shelf pressure to attempt to compensate for changes in the SSH during the forward run.
We have found this approach to be robust over a range of resolutions from <1 km to 240 km and in both idealized and realistic model configurations.