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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. The Goal. Estimation of pan-Antarctic sea ice algal production. The Model. Atmosphere forced by ECMWF reanalysis - PowerPoint PPT Presentation
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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