Modify land ice melt equations

[cbegeman]

This PR includes two changes to the 3-equation parameterization for ice-shelf basal melting in MPAS-Ocean:

1. Assume that melted land ice enters at the interface temperature. Thus, we can remove the sensible heat flux associated with raising the meltwater from iceTemperature to the interface temperature (mistakenly assigned to the freezing point at local pressure and zero salinity).
2. Add a conductive heat flux term to the heat conservation equation. We assume that this term will come from MALI and have no dependence on the interface temperature on the MPAS-Ocean time step at which it appears in the 3-equation parameterization. (Note that this does not preclude the conductive heat flux from depending on the interface temperature from a previous MPAS-Ocean time step or, preferable, the previous coupling interval.) Thus, this term can be added to the c term of the quadratic equation. (If it depended on the interface temperature it would need to be added to the b term.)

[cbegeman]

@xylar Do you want to take a quick look at the code before I proceed with testing and let me know if this looks like what we agreed upon?

[xylar]

Let's chat about this when we meet today. I think the units as written don't quite work out.

[cbegeman]

@xylar I think I addressed your comments with the latest commits. Resolve if you're happy. Still not yet tested.

[xylar]

I think this looks good. Just one issue I'd like to resolve with 2 confusing local variable names.

[cbegeman]

@xylar Just noting that I changed the sign of the advective heat flux for all melt routines. E.g., for the ISOMIP+ test case, heatFluxToLandIce was positive and it should be negative because landIceInterfaceTemperature < 0 and landIceFreshwaterFlux > 0. It doesn't change the solution because we hadn't actually been using heatFluxToLandIce. 49d3b44

[cbegeman]

Testing

Key points:

• This branch slightly amplifies both land ice melting and land ice frazil formation (by ~0.5%)

Conservation statistics are daily; reported for 0001-02-01

ENERGY CONSERVATION CHECK
   HEAT FLUXES: explicit
   MPAS-Ocean name            W (raw sum)    coupler name    short name         W/m^2 (flux/A)
MASS CONSERVATION CHECK  
   MASS FLUXES
   MPAS-Ocean name          kg/s (F)       coupler name     short name     kg/m^2/s*1e6 (F/A)

B-case, this branch, conductive flux
Results not yet available

B-case, this branch, no conductive flux
/lcrc/group/e3sm/ac.cbegeman/scratch/chrys/20251030.GMPAS-JRA1p5-DIB-PISMF.TL319_SOwISC12to30E3r4.modify-melt.chrysalis/run

landIceHeatFlux           -1.19110710E+13                                      -0.02335048
      landIceFrazilHeatFlux   5.16040508E+10 (already in hfreeze, do not sum                )      0.00010116
landIceFreshwaterFlux    3.52572738E+07                                       0.06911840
     landIceFrazilFlux     -1.54642046E+05 (already in wfreeze, do not sum                )     -0.00030316

B-case, master
/lcrc/group/e3sm/ac.cbegeman/scratch/chrys/20251030.GMPAS-JRA1p5-DIB-PISMF.TL319_SOwISC12to30E3r4.master.chrysalis/run

 landIceHeatFlux           -1.19889658E+13                                      -0.02350318
      landIceFrazilHeatFlux   4.88409855E+10 (already in hfreeze, do not sum                )      0.00009575
 landIceFreshwaterFlux    3.50634480E+07                                       0.06873842
     landIceFrazilFlux     -1.46361958E+05 (already in wfreeze, do not sum                )     -0.00028693