A quasi-empirical, macro-scale method for slush ice desalination

1. A quasi-empirical, macro-scale method for slush ice desalination Benjamin Saenz & Kevin Arrigo Department of Environmental Earth System Science Stanford University

2. The Goal • Estimation 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 …

3. Gravity Drainage Brine Volume Flux (Vconv) Simple brine replacement/dilution: Desalination-dependent volume flux: Eularian volume based mixing of flux volume between layers Meltwater Flushing Instantaneous volume replacement

4. Slush • Why slush? • Algae like it warm and porous • Flooding observed over 30% of Antarctic ice floes • Gap/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

5. Ice Station Weddell – Site B Fristen et al. 1994; Lytle & Ackley 1996; Ackley et al. 1996

6. The slush problem

7. The slush fix • Fristen et al. 1998, Andreas et al. 2004 (ISW Site B models) = remove salt, hold t constant until appropriate ice volume has frozen • No desalination estimate • No way to estimate instantaneous brine flux • Me: Assume slush layer is the effective thermal ‘bottom’ of the ice sheet (kind of the same)

8. ‘Interface’ desalination • dh/dt in slush is not straightforward for ds/dt calculation – re-classify stable salinity in terms of heat flux (assuming constant T)

9. Heat Flux ‘Stable Salinity’ Ice Growth Desalination Brine Flux

10. fcrit = 0.2 @ T= -1.9, S = 0.2*(-1.9/-0.054) S = 7 psu bulk Large brine tubes

11. Looks good

13. Brine Flux Volumes Stable-salinity based: (more or less tuned…but sufficient for biology) Total = 10.4x turnover, within 4-18x estimated by Ackley et al. 1996 Cox/Weeks gravity drainage based: 4.5x10-7 – 5x10-8, with measurement range 3.4x10-7 – 1x10-8 (Wakatsuchi 1984; Reeburg 1984)

14. Another application: Frazil ice desalination 5cm initial frazil layer 18psu Isothermal at seawater T

15. 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

16. Thought: • 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? Snow ice salinity (diamonds) Maksym and Jeffries 2001

17. 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)

18. Still more thoughts • Convective 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?

19. Permeability: 3 orders of magnitude Darcy’s law: velocity is inverse of permeability Velocity: 3 orders of magnitude Golden et al. 2007

20. Notz and Worster 2008