The Ice-Ocean Interface Miles McPhee McPhee Research

1. The Ice-Ocean InterfaceMiles McPheeMcPhee Research • Anecdotal history • Heat and salt transfer (freezing) • Heat and salt transfer (melting)

2. Maykut, G.A., and N. Untersteiner, 1971. Some results from a time-dependent thermodynamic model of sea ice, J. Geophys. Res., 76, 1550-1575.

3. Greenland Estimates of upward heat flux out of the Atlantic layer based on temperature changes and circulation, adapted from Treshnikov and Baranov (1972, Water circulation in the Arctic Basin) Alaska

4. McPhee, M.G., and N. Untersteiner, 1982. Using sea ice to measure vertical heat flux in the ocean. J. Geophys. Res., 87, 2071-2074.

7. Perovich, D. K., and B. Elder. Estimates of ocean heat flux at SHEBA, Geophys. Res. Lett., 29 (9), doi: 10.1029/2001GL014171, 2002.

8. Martin, S., P. Kauffman, and C. Parkinson, 1983: The movement and decay of ice edge bands in the winter Bering Sea, J. Geophys. Res.,88, 2803-2812. . Initial ice thickness, 1.2 m

10. My theory for ice edge bands (McPhee, M.G.. J. Geophys. Res., 88, 2827-2835, 1983): rapidly melting ice stabilizes the OBL, reducing its effective drag. The band separates from the pack because the leading edge always encounters warm water and rapidly cools the water as it passes over.

11. water Thermal Balance at the Ice/Ocean Interface Ice Advection into control volume Thermal conduction into ice w=w0+wp T0, S0 Latent heat source or sink Turbulent heat flux from ocean Advection out of control volume

12. Heat Equation at the Ice/Ocean Interface • Heat conduction through the ice • Sensible heat from percolation of fresh water through the ice column • Latent exchange at the interface • Turbulent heat flux from (or to) the ocean Small

13. Heat conduction through the ice

14. Latent heat exchange at the interface Turbulent ocean heat flux

15. Salt Balance at the Ice/Ocean Interface Advection into control volume Ice Sice w=w0+wp S0 Turbulent salt flux from ocean Advection out of control volume

16. small “Kinematic” Interface Heat Equation Interface Salt Conservation Equation Interface freezing condition

17. w0~1/2 to 1 m/day dT=2 K dT=1 K Inertial periods Mellor, G.L., M.G. McPhee, and M. Steele. 1986. Ice-seawater turbulent boundary layer interaction with melting or freezing. J. Phys. Oceanogr., 16, 1829-1846.

18. “Throughout the mixed layer the [MY2-1/2 model] calculations produced a small amount of supercooling, implying the creation of frazil ice. The process may be understood as follows. Over the domain of the model the average change in salinity is the time integral of the surface salinity flux, since there is no flux at the bottom. Similarly, the average change in temperature is the time integral of kinematic heat flux. If the entire water column started at its (surface) freezing point, it will remain on the freezing line if the ratio of surface fluxes … is equal to m. This will be true only if the eddy diffusivities and surface roughnesses for heat and salt, z0t and z0S, are equal. In the model, the temperature surface roughness is larger than the salinity roughness, which means that across the surface layer heat is transported faster than salt, supercooling the water column. The effect is small. In these calculations, if the supercooled water were restored to equilibrium, the amount of frazil production amounts to only a half percent of the total.”

22. The first direct measurements of turbulent heat flux in the ocean were made from drifting ice north of Fram Strait during the 1984 MIZEX project.

25. measured ablation rates model w/laminar sublayers

26. SHEBA From: McPhee, Kottmeier, Morison, 1999, J. Phys. Oceanogr., 29, 1166-1179. A simpler approach is just to assume that a bulk heat exchange coefficient describes the exchange:

27. “Throughout the mixed layer the [MY2-1/2 model] calculations produced a small amount of supercooling, implying the creation of frazil ice. The process may be understood as follows…The effect is small…” No longer true! Now it amounts to about a third!

28. Growth with frazil accretion Straight congelation growth Holland et al. found in their coupled model that frazil accretion under different ice types resulted in increased equilibrium thickness Holland, M. M., J. A. Curry, and J. L. Schramm, 1997: Modeling the thermodynamics of a sea ice thickness distribution 2. Sea ice/ocean interactions, J. Geophys. Res., 102, 23,093-23,107

29. Freezing

30. Impact of exchange coefficient ratio on freezing with

31. Collaborative Study of Ice-Ocean Interaction in Svalbard Supercoolometer Turbulence Mast Ice Temperature & Solid Fraction

32. Van Mijen Fjord Instruments SonTek Instrument Cluster 0.6 m Ice T-string SBE 04 conductivity meter 1 m SBE 03 thermometer ROV- CTD SBE 07 micro-conductivity meter SonTek ADVOcean (5 MHz)

33. Supercoolometer: Seamore ROV SBE 39 T Probe Optical Backscatter Water In Heater SBE-19+ Temperature & Conductivity

34. Heat and Salt Fluxes at 1 m Below Ice

35. Temperature Profiles in Ice:Range of Possible Heat Fluxes, q

36. Ice Balance:Only matches ocean fluxes for a near 1 ah/as ah/as VanMijenFjord conditions: u*=0.003 m s-1, S=34.2 psu, T at freezing

37. No Boundary Layer Supercooling at Van Mijen Fjord

38. Simulations for a=1 agree with observed profiles of T-Tf Simulations for a=40 disagree with observed profiles of T-Tf

39. How could Cs= Ch? Implies fluxes are not dependent on diffusion across molecular sublayers, w’, T’,S’ = 0 at interface. Answer: The growing ice is a mushy layer with active convection. Mushy layers can be viewed as the consequence of morphological instabilities of would-be planar solid-liquid phase boundaries (Mullins & Sereka, 1964), and serve to reduce or eliminate regions of constitutional supercooling in the system (Worster, 1986; Fowler, 1987) that arise due to the slow diffusion of chemical species relative to heat. Worster, 1992Worster, M.G., 1992, The Dynamics of Mushy Layers, in Interactive Dynamics of Convection and Solidification, Davis, Huppert, Muller and Worster eds., Kluwer Academic Publishers, London

40. Melting

41. Serendipity: Dirk’s Problem After the UNIS 2000 AGF211 course, a student Dirk Notz contacted me asking if I could recommend a suitable air/sea/ice interaction problem for a Master’s thesis at the U. Hamburg. I tentatively suggested he look at the “false bottom” question. He did: Notz et al., 2003, J. Geophys. Res.

42. During the 1975 AIDJEX Project in the Beaufort Gyre, Arne Hansonmaintained an array of depth gauges at the main station Big Bear. Hereare examples showing a decrease in ice thickness for thick ice, but an increase at several gauges in initially thin ice.

43. Thick ice (BB-4 – BB-6) ablated 30-40 cm by the end of melt season. “Falsebottom” gauges showed very little overall ablation during the summer. The box indicates a 10-day period beginning in late July, when false bottoms apparently formed at several sites.

44. Assuming a linear temperature gradient in the thin false bottom: If the upper layer is fresh, at temperature presumably near freezing:

45. This modifies the heat equation slightly,but leads to a similar quadratic for S0

46. Changes in icebottom elevationrelative to a referencelevel on day 190, atthe “false bottom” sites. Estimated frictionvelocity for differentvalues of bottom surface roughness,z0 = 0.6 and 6 cm respectively Note that false bottoms appear to form at all sites during the relative calmstarting about day 205, and start migrating upward on or near day 210, whenthe wind picks up