RK time stepping does not allow global budgets to close

[trhille]

When using RK schemes, the budget components reported in global stats do not allow the global budget to close.
Here is a Thwaites 4–20km run using foward Euler, in which the global budget closes to ~machine precision:

And the same run using RK2, which has a fractional error of 50%:

(Figures made using the first part of https://github.com/trhille/MPAS-Tools/blob/update_plot_mass_balance/landice/output_processing_li/plot_mass_balance.py.

I don't think this is an issue with actual mass conservation, but more likely because there should be accumulated calvingThickness from restore-calving in the RK loop, here. However, this is then being zeroed out when calling the main calving routine later, which starts by zeroing out the calving thickness here.

[trhille]

Perhaps the issue is a little more fundamental than this. In a run using RK2 without any calving (i.e., no restore calving, no remove icebergs, no remove islands) and no face-melting, there is still a ~10% mass imbalance:

This might require a refactoring of the RK loop to use this form:

instead of this lower-storage form:

(equations from Shu & Osher, 1988)

[trhille]

Using PRs 140, 141, and 142 together, we are able to close the mass budget in a run with BMB, SMB, restore-calving, and face-melting:

However, if we add a rate-based calving law, we no longer conserve mass. This is because calvingThickness is overwritten by li_apply_ablation_velocity when it is passed into ablationThickness.