hocn calculation and flushing velocity issue

[davidclemenssewall]

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PR checklist

• Short (1 sentence) summary of your PR:
  Fixes two small bugs related to how the mass of melt pond water impacts melt pond drainage and synchronizes 'apnd' nomenclature.
• Developer(s):
  @davidclemenssewall
• Suggest PR reviewers from list in the column to the right.
  @dabail10 @eclare108213 @apcraig
• Please copy the PR test results link or provide a summary of testing completed below.
  Ran the Icepack base_suite on conda_linux with a baseline comparison to a baseline from the latest 'main' branch. All tests passed except the comparison tests for cases that used mushy thermodynamics and level or topo ponds (see below). These tests were expected to fail due to the nature of this code change. I have not been able to test the impacts of these changes in CICE because the current icepack main branch fails to compile in CICE.
  FAIL conda_linux_smoke_col_1x1_diag1_run1year compare icepack.main different-data
  FAIL conda_linux_smoke_col_1x1_debug_run1year compare icepack.main different-data
  FAIL conda_linux_smoke_col_1x1_bgcispol_debug compare icepack.main different-data
  FAIL conda_linux_smoke_col_1x1_bgcnice_debug compare icepack.main different-data
  FAIL conda_linux_smoke_col_1x1_debug_zaero compare icepack.main different-data
  FAIL conda_linux_smoke_col_1x1_debug_run1year_swredist compare icepack.main different-data
  FAIL conda_linux_smoke_col_1x1_debug_dt30min_leap_run1year compare icepack.main different-data
  FAIL conda_linux_smoke_col_1x1_debug_dyn_run1year compare icepack.main different-data
  FAIL conda_linux_smoke_col_1x1_debug_fsd12_run1year_short compare icepack.main different-data
  FAIL conda_linux_smoke_col_1x1_debug_fsd1_run1year compare icepack.main different-data
  FAIL conda_linux_smoke_col_1x1_debug_run1year_snw30percent_snwgrain compare icepack.main different-data
  FAIL conda_linux_smoke_col_1x1_debug_run1year_snwitdrdg compare icepack.main different-data
  FAIL conda_linux_smoke_col_1x1_calcdragio_debug_run1year compare icepack.main different-data
  FAIL conda_linux_smoke_col_1x1_debug_modal_run1year compare icepack.main different-data
  FAIL conda_linux_smoke_col_1x1_debug_fluxopenw_run1year compare icepack.main different-data
  FAIL conda_linux_smoke_col_1x1_debug_dyn_fluxopenw_run1year compare icepack.main different-data
  FAIL conda_linux_smoke_col_1x1_debug_run1year_snicartest compare icepack.main different-data
  FAIL conda_linux_smoke_col_1x1_debug_run1year_snicar compare icepack.main different-data
  FAIL conda_linux_smoke_col_1x1_congel_debug_run1year compare icepack.main different-data
  FAIL conda_linux_restart_col_1x1_debug compare icepack.main different-data
  FAIL conda_linux_restart_col_1x1_diag1 compare icepack.main different-data
  FAIL conda_linux_restart_col_1x1_pondlvl compare icepack.main different-data
  FAIL conda_linux_restart_col_1x1_pondtopo compare icepack.main different-data
  FAIL conda_linux_restart_col_1x1_bgcispol compare icepack.main different-data
  FAIL conda_linux_restart_col_1x1_bgcnice compare icepack.main different-data
  FAIL conda_linux_restart_col_1x1_snwgrain_snwitdrdg_zaero compare icepack.main different-data
  FAIL conda_linux_restart_col_1x1_isotope compare icepack.main different-data
  FAIL conda_linux_restart_col_1x1_saltflux compare icepack.main different-data
  FAIL conda_linux_restart_col_1x1_dyn compare icepack.main different-data
  FAIL conda_linux_restart_col_1x1_fsd12_short compare icepack.main different-data
  FAIL conda_linux_restart_col_1x1_snwgrain_snwitdrdg compare icepack.main different-data
  FAIL conda_linux_restart_col_1x1_modal compare icepack.main different-data
  FAIL conda_linux_restart_col_1x1_fluxopenw compare icepack.main different-data
  FAIL conda_linux_restart_col_1x1_snicartest compare icepack.main different-data
  FAIL conda_linux_restart_col_1x1_snicar compare icepack.main different-data
  FAIL conda_linux_restart_col_1x1_congel compare icepack.main different-data
  36 of 215 tests FAILED
• How much do the PR code changes differ from the unmodified code?
  • bit for bit
  • different at roundoff level
  • more substantial
• Does this PR create or have dependencies on CICE or any other models?
  • Yes
  • No
• Does this PR add any new test cases?
  • Yes
  • No
• Is the documentation being updated? ("Documentation" includes information on the wiki or in the .rst files from doc/source/, which are used to create the online technical docs at https://readthedocs.org/projects/cice-consortium-cice/.)
  • Yes
  • No, does the documentation need to be updated at a later time?
    • Yes
    • No
• Please document the changes in detail, including why the changes are made. This will become part of the PR commit log.
  Currently, there are two bugs in how icepack computes the height of the ocean above the ice base in icepack_therm_mushy.F90 line 3141:

hocn = (ice_mass + hpond * apond * rhow + hsn * rhos) / rhow

First, rhow is the density of ocean water, but ponds that depress the ice surface are generally found to be fresh water. Thus, rhow in the numerator should be replaced by rhofresh.
Second, apond here is the category pond area tracer, however it is being treated as the category pond area fraction (see footnote below). For the level-ice scheme, the category pond area fraction is apnd*alvl.
This PR fixes both issues. There were also offsetting errors in the flushing_velocity and flush_pond subroutines that have been fixed.

I believe that the second bug was made more likely by using inconsistent naming conventions for the pond area tracer and pond area fraction. In icepack_meltpond_lvl.F90 and other parts of the code base, it appears that the general convention is to use apnd to denote the pond area tracer and apondn for the category or full-grid-cell pond area fraction (i.e., apondn = apnd*alvl for the level pond scheme). I propose that we follow this convention throughout the code base, such that apnd always refers to the pond area tracer. This PR makes these changes in the mushy and vertical thermodynamics modules.

Footnote: there is an alternate interpretation of using just the pond area tracer in the numerator for the level pond scheme which is that the level areas of an ice category separated from the deformed areas by borders of zero flexural rigidity (i.e., the thicker, pond-free, deformed ice cannot provide any upward buoyancy force to the level, ponded areas). If this is the intention, then I think we need to also use the level ice volume (vlvl) in the calculation of ice mass and the level-ice snow depth for consistency.

[dabail10]

Here are the results of the QC test. Everything passes. This will only change answers when ponds are on. Yes, level ponds are on in the two simulations even though they don't really look that different.

[apcraig]

fix indentation

[davidclemenssewall]

Done.

[apcraig]

Suggest moving alvl up in the calling arguments. Makes no difference technically, but seems like it belongs with apnd and hpond, for instance.

[davidclemenssewall]

Done.