Should LinearLiquidus depend on depth/pressure?

[glwagner]

Right now it just depends on salinity:

ClimaSeaIce.jl/src/SeaIceThermodynamics/SeaIceThermodynamics.jl

Lines 23 to 32 in fd73907

	LinearLiquidus(FT=Float64,
	slope = 0.054, # psu / ᵒC
	freshwater_melting_temperature = 0) # ᵒC
	Return a linear model for the dependence of the melting temperature of
	saltwater on salinity,
	```math
	Tₘ(S) = T₀ - m S ,
	```

but we actually may want to incorporate depth dependence for various reasons.

cc @colinrmeyer @jbuffo

[jbuffo]

For the depths sea ice experiences you probably wouldn't need it, given the delta_Tm for being beneath 1km of ice is around 1C. But if you want to generalize the code for use under thicker ices, then I would look into the Thermodynamic Equation Of Seawater (TEOS) literature as I think they have good freezing point polynomial approximations up to 100MPa

[glwagner]

I think the main application is not at the base of the sea ice but rather to more accurately describe the formation of frazil ice, which involves a combination of cooling and turbulent mixing that can require the liquidus to be applied some depth below the surface (depending on the strength of the turbulent mixing). Skyllinstad and Denbo (2001) for example suggest that capturing this physics matters:

https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/1999JC000091

but I am wondering what you think about that!

[jbuffo]

Sweet, then yeah, the pressure dependence would be great to include. The thermal driving leading to frazil and platelet ice is usually only on the order of tens of millikelvin, so having a model that would be sensitive to this would be sick!

[glwagner]

🔥

I also think that this would actually make the code easier to understand. For frazil we have to compute the melting temperature everywhere in the water column. Even if it doesn't matter much, I think it will simply make more sense and be easier to understand if the melting temperature is correct in this very simple way (depends on z).