1. Ice/Ocean Interaction Part 1- The Ice/Ocean Interface 1.Background, rationale 2.Enthalpy and salt balance at the interface 3.The “Three-Equation” Interface Solution 4.Heat Flux Measurements and the Stanton Number for Sea Ice 5.Double-Diffusion and Melting 6.False Bottoms 7.Freezing: Is Double Diffusion Pertinent? 8.Summary

2. Basal (Ocean) Heat Flux Relatively small changes in open water fraction when sun angle is high are a major source of variability in the total surface heat balance. It is a misconception that mixed layers are like ice baths maintained at freezing temperature– in summer the Arctic mixed layer is typically several tenths of a degree above freezing, even in high ice concentrations. Under seasonal ice of the Weddell Sea, the mixed layer is nearly always at least 8-10 mK above freezing. In the perennial ice pack of the Arctic, transfer of heat from the ocean to the ice occurs mainly in summer, and in aggregate is as important in the overall heat balance as either the net radiative flux, or sensible and latent heat flux at the upper surface.

3. Day of 2002 NPEO JCAD/NPS BUOY 2002

4. McPhee et al., 2003, Geophys. Res. Lett.

5. Ice water Thermal Balance at the Ice/Ocean Interface w=w 0 +w p Turbulent heat flux from ocean Thermal conduction into ice T 0, S 0 Latent heat source or sink

6. Heat Equation at the Ice/Ocean Interface Heat conduction through the ice Latent exchange at the interface Turbulent heat flux from (or to) the ocean

7. Heat conduction through the ice

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

9. w=w 0 +w p Turbulent salt flux from ocean Advection into control volume Advection out of control volume Ice Salt Balance at the Ice/Ocean Interface S 0 S ice Interface Salt Conservation Equation

10. Parameterize turbulent flux of a quantity as proportional to the product of a scale velocity and and change in the quantity from the boundary to some reference level. Multiyear pack ice: z 0 = 5 cm, d = 2 m (surface layer).

11. Assume analogous expressions for scalar fluxes: For multiyear ice, the corresponding melt rate would be about 1.3 m per day. During MIZEX 84 in the Fram Strait marginal ice zone we experienced melt rates of ~ 7 cm per day in conditions like these. If by Reynolds analogy Suppose u *0 = 0.01 m s -1, and  T = 1 K.

12. Near the end of MIZEX we crossed an ocean front as the ice drifted south in response to a small storm. The mixed layer temperature rose abruptly, with rapid increase in basal melting. McPhee, Maykut, Morison, J. Geophys. Res., 1987 On day 191, the average  T > 1 K, and melt rate was around 7 cm per day.

13. If Reynolds analogy doesn’t work, resort to dimensional analysis By the Pi Theorem five governing parameters, three with independent dimensions:

14. The Blasius solution for the laminar momentum and scalar contaminant boundary layers: Where the Stanton number is the kinematic heat flux divided by the product of the far-field velocity and  T. Exponents are p =1/2 and n = 2/3. Owen and Thomson (1963) and Yaglom and Kader (1974) investigated heat and species concentration fluxes in laboratory flows over rough surfaces: OT: p =0.45 and n = 0.8 YK: p =1/2 and n = 2/3

15. The “three-equation” interface model: Prescribe Unknowns: Third equation: Combine into a quadratic formula for S 0

16. “Temperature Scales:” “Sensible”: “Latent”: “Percolation”: small

17. “Two equation” approach Assumption:  T=T w -T 0 can be approximated by the departure of mixed layer temperature from freezing, i.e., that interface temperature is approximately the mixed layer freezing temperature. T 0 and S 0 are difficult to measure directly, but suppose the following:

19. From McPhee, Kottmeier, Morison JPO 1999

20. Yaglom-Kader Re * dependence

21. When is small, the quadratic solution depends on the ratio of exchange coefficients which is a measure of the strength of double diffusion. R = 1: heat and salt exchange is similar. Salt will enter the control volume at a rate necessary to keep R >> 1: salt flux is inhibited relative to heat and the thermal driving is reduced. Melting is rate limited by double- diffusive effects in the transition sublayers.

22. Thought experiment: Using St * = 0.0057 (SHEBA average), the bulk formula basal heat flux is 34 W m -2. For R =1 and R = 70, find the  h values that provide the same 34 W m -2 heat flux.

23. Now repeat the exercise using keeping the same values for  h and  S as for the modest thermal forcing. Respective melt rates are about 22 and 32 cm per day

24. false bottom “true” bottom “water table” The False Bottom Problem Notz et al., J. Geophys. Res., 2003.

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

26. Thick ice (BB-4 – BB-6) ablated 30-40 cm by the end of melt season. “False bottom” 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.

27. Estimated friction velocity for different values of bottom surface roughness, z 0 = 0.6 and 6 cm respectively Changes in ice bottom elevation relative to a reference level on day 190, at the “false bottom” sites. Note that false bottoms appear to form at all sites during the relative calm starting about day 205, and start migrating upward on or near day 210, when the wind picks up

29. Assumptions: The upper water layer and the false bottom ice layer are fresh The fresh water layer temperature is 0 o C The temperature gradient in the false bottom is linear. where h is the total thickness of the false bottom. The upper surface will then migrate upward at a rate The kinematic heat flux in the false bottom ice is then downward:

30. The time rate of change of thickness of the false bottom will then be The quadratic equation for the lower interface is similar to earlier but modified for the different ice heat flux condition:

35. false bottom “true” bottom upward heat flux down “water table” Aside from maybe helping us estimate  h, are false bottoms of more than academic interest? They are effective at shielding thin ice from ocean heat hence potentially important for ice-albedo feedback 1 They are like radiators pumping heat into the mixed layer rather than sucking it out. 2

38. Summary for melting  Transport of salt across the interface is much slower than heat, and effectively controls the melting rate  The exchange ratios for heat and salt (  h and  S ) are difficult to measure, but are constrained by the bulk Stanton number, which is measurable  Collection of fresh water in irregularities in the ice undersurface both protects thin ice from melting and slows the overall heat transfer out of the mixed layer. This retards (provides a negative feedback to) the summer ice-albedo feedback

39. Double Diffusion during Freezing: A Mechanism for Supercooling or Frazil Ice Production? If the same sort of double diffusion occurs in the upper ocean (transition sublayers) during freezing, then if heat leaves the upper ocean faster than salt enters, there is potential for supercooling, and if nucleation sites are available, for accumulation of frazil ice.

40. Impact of exchange coefficient ratio on freezing with

41. Straight congelation growth Growth with frazil accretion

43. SonTek ADVOcean (5 Mhz) SBE 03 thermometer SBE 07 microstructure conductivity meter SBE 04 conductivity meter SonTek Instrument Cluster

47. We made measurements as part of the primary experiment from day 67 to 70, then during the UNIS student project a week later. Using the observation that the ice was hydraulically smooth we can estimate the stress from a current meter that recorded continuously at 10 m depth, giving us a 24-day record to provide the momentum forcing for a numerical model.

48. During the initial project, the temperature gradient near the base of the ice indicated a conductive heat flux of around 20 W m -2. We used this as a constant flux in the model, shown above for 3 different values of R. The dashed line is the mean growth rate determined by comparing the ice thickness measured at the start and end of the period. The second plot shows the modeled and observed salinity.

49. From the numerical model we can estimate the turbulent heat flux 1 m below the interface for the various R values, then compare the model output with measurements made during the two observation period. This provides strong evidence that the double-diffusive effect is very small (R = 1) when ice is freezing.

50. Conclusions During melting, double diffusion effects are paramount, and ice dissolves as much as it melts False bottoms (a) may protect thin ice from the impact of ocean heat flux during summer; (b) provide a means of determining the ratio of diffusivities appropriate for melting ice. During freezing, it appears that double diffusive tendencies are relieved near the interface by differential ice growth, so that supercooling and frazil production are limited during congelation growth