A quasi-empirical, macro-scale method

for slush ice desalination

Benjamin Saenz & Kevin ArrigoDepartment of Environmental Earth System

ScienceStanford University

The GoalEstimation of pan-Antarctic sea ice algal

production

The Model Atmosphere forced by ECMWF reanalysis

Bitz and Lipscomb 1999 heat transfer, Pringle et al. 2007 conductivity

Cox and Weeks 1988 / Petrich et al. 2006 re-interpretation of empirical desalination

Sophisticated algal model (Arrigo et al. 1994 + detritus, remineralization)

32 wavelength delta-Eddington shortwave radiation transfer, supplied by Gregg and Carder clear-sky model

Brine flux …

Gravity Drainage Brine Volume Flux (Vconv)

€

dS i

dt= Vconv

i (Sbi+1 − Sb

i )

€

Vconvi =

dS i

dt

1

Sbi+1 − Sb

i

Simple brine replacement/dilution:

Desalination-dependent volume flux:

Meltwater Flushing

Instantaneous volume replacement

Eularian volume based mixing of flux volume between layers

Slush

Why slush? Algae like it warm and porousFlooding observed over 30% of Antarctic ice floesGap/surface communities estimated to contribute

bulk of Antarctic primary production ( ? )

Test case: Ice Station Weddell, a data set comprising temperature, salinity, algae, nutrients, atmospheric forcing, and Steve Ackley

Ice Station Weddell – Site B

Fristen et al. 1994; Lytle & Ackley 1996; Ackley et al. 1996

The slush problem

The slush fixFristen et al. 1998, Andreas et al. 2004 (ISW Site

B models) = remove salt, hold t constant until appropriate ice volume has frozenNo desalination estimateNo way to estimate instantaneous brine flux

Me: Assume slush layer is the effective thermal ‘bottom’ of the ice sheet (kind of the same)

‘Interface’ desalinationdh/dt in slush is not straightforward for ds/dt

calculation – re-classify stable salinity in terms of heat flux (assuming constant T)

‘Stable Salinity’Heat Flux Ice Growth

Desalination

Brine Flux

crit

@ T= -1.9,S = 0.2*(-1.9/-0.054)S = 7 psu bulk

Large brine tubes

Looks good

Brine Flux Volumes

Total = 10.4x turnover,within 4-18x estimated by Ackley et al. 1996

Stable-salinity based: (more or less tuned…but sufficient for biology)

Cox/Weeks gravity drainage based: 4.5x10-7 – 5x10-8, with measurement range 3.4x10-7 – 1x10-8 (Wakatsuchi 1984; Reeburg 1984)

Another application:Frazil ice desalination

5cm initial frazil layer18psuIsothermal at seawater T

Observations

Brine fluxes seem constrained

Algae grow with the correct vertical distribution

Final bulk salinity is above stable salinity predicted by heat flux some fluid extra fluid resistance compared to ice bottom

Desalination proceeds at a rate equal to bottom desalination

Prescribed final salinity of 6ish/0.2 brine fraction – this must describe the permeability of underlying ice. Is this generalizable? No but at longer timescales?

Thought:

Snow ice salinity (diamonds)Maksym and Jeffries 2001

More Thoughts:Convective heating – what is the effect of having a

large slush layer – is there extra conductive heat flux to a large slush layer? does cold brine gain more heat from surrounding ice?

How does the underlying porosity effect final slush salinity? Large brine tubes?

Can mushy layer models give some simple relationships between underlying porosity and slush layer desalination? (slow growth under snow)

Still more thoughtsConvective heat flux – seawater temp above

freezing? Ice station Weddell: -1.7 w/ 34.1 psu = not freezing.

Fluid resistance at ISW – was the brine-tube riddled ice below providing the resistance, or the slush itself, or the brine tube spacing/pooling at slush layer bottom?

Golden et al. 2007

Permeability: 3 orders of magnitudeDarcy’s law: velocity is inverse of permeabilityVelocity: 3 orders of magnitude

Notz and Worster 2008