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A quasi-empirical, macro- scale method for slush ice desalination Benjamin Saenz & Kevin Arrigo Department of Environmental Earth System Science Stanford University
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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 …
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Gravity Drainage Brine Volume Flux (V conv ) Simple brine replacement/dilution: Desalination-dependent volume flux: Meltwater Flushing Instantaneous volume replacement Eularian volume based mixing of flux volume between layers
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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
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Ice Station Weddell – Site B Fristen et al. 1994; Lytle & Ackley 1996; Ackley et al. 1996
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The slush problem
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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)
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‘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)
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‘Stable Salinity’Heat FluxIce Growth Desalination Brine Flux
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crit @ T= -1.9, S = 0.2*(-1.9/-0.054) S = 7 psu bulk Large brine tubes
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Looks good
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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)
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Another application: Frazil ice desalination 5cm initial frazil layer 18psu Isothermal at seawater T
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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
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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
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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)
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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?
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Golden et al. 2007 Permeability: 3 orders of magnitude Darcy’s law: velocity is inverse of permeability Velocity: 3 orders of magnitude
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Notz and Worster 2008
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