1. Ice Sheets and Glaciers in the Climate System 11–22 September 2007, Karthaus, Italy Interaction of Ice Shelves with the Ocean Adrian Jenkins British Antarctic Survey, Natural Environment Research Council, Cambridge, U.K.

2. Part I: i.Introduction to the problem ii.Impact of melting ice on the ocean iii.Circulation and melting beneath ice shelves iv.Impacts of climate change Part II: Ice sheets, ice shelves and the oceans that surround them. Interactions between freshwater ice and seawater. Some theory and model results. How could atmospheric change reach the base of an ice shelf?

3. (i) Introduction to the problem They form where the ice sheet margins are not thick enough to remain grounded on the seabed. Ice shelves are primarily associated with “marine ice sheets”, which rest on a bed that lies below sea level. Presently most ice shelves are in Antarctica, especially West Antarctica. (a) Ice sheets and ice shelves

4. Snow falling in the interior of the ice sheet is ultimately lost from the ice shelves by iceberg calving and basal melting. The ocean plays a key role in both processes of mass loss. In these lectures we will consider the process of basal melting.

5. Ice shelves comprise 13% of the Antarctic Ice Sheet and receive 80% of the discharge from the grounded ice. Antarctica gains 2200±200 Gt yr -1 by surface accumulation. Iceberg calving removes 2100±300 Gt yr -1. Ice shelf (net) melting removes 700±200 Gt yr -1 (~15-35% of loss). The ice shelves also play a role in regulating the discharge of grounded ice.

6. The thickness of the ice shelves evolves in response to surface accumulation, vertical strain and basal melt/freeze. Accumulation rate 0 to 0.1 m yr -1 (observed) Vertical strain rate -1 to 1 m yr -1 (observed) Melt/freeze rate -1 to 10 m yr -1 (usually inferred from the other two and an assumption of steady state) Typical orders of magnitude:

7. Ice shelves along the Antarctic Peninsula have shown dramatic retreat in recent years. (Source: Rignot, 2006, http://copes.ipsl.jussieu.fr/Workshops/SeaLevel/OralPresentations/index.html) A large part of Larsen B Ice Shelf disintegrated in the space of three weeks in early 2002. Following loss of the ice shelves the glaciers that fed them have accelerated and thinned.

8. Ice shelf disintegration appears to be correlated with air temperatures. South of the line of stability thinning has been observed. This may have an oceanic origin. When the surface becomes warm enough to melt in summer the ice shelf becomes unstable. Isotherms of mean annual surface temperature

9. In the Amundsen Sea, well south of the line of stability, ice shelves are thinning rapidly. The widespread, coherent nature of the thinning suggests oceanic forcing. The thinning has propagated inland of the grounding line and ice stream discharge has increased. [Shepherd et al., GRL, 2004] This makes a direct contribution to sea level rise (~5% of current rate). The rates of change are not steady. On Pine Island Glacier two periods of acceleration were separated by a quiescent phase from 1987-94.

10. Atmospheric circulation is driven by differential solar heating. The north/south flows redistribute the heat towards higher latitudes. The result is a banded structure of easterly and westerly winds. The surface flows go from high to low pressure, but are deflected by the Coriolis force. (Source: http://en.wikipedia.org/wiki/Atmospheric_circulation) (b) The Southern Ocean

11. (Source: http://en.wikipedia.org/wiki/Atmospheric_pressure) Mean sea level pressure (JJA) Mean sea level pressure (DJF) Over the Southern Ocean the pressure pattern and prevailing winds are undisturbed by land. The result is the vast clockwise circulation of the Antarctic Circumpolar Current. Because there is a net surface transport to the left (in the southern hemisphere) of the winds, the low pressure regions around Antarctica are zones of upwelling.

12. Southward flow of deep waters and northward flow of AAIW and AABW are major components of the meridional overturning circulation. To the south of the ACC deep waters are raised toward the surface. Cooling and freshening produces intermediate waters. Intense cooling in the far south produces bottom waters.

13. Transformation of deep waters occurs through interaction with ice and atmosphere. There is a net freshwater input because precipitation exceeds evaporation and is supplemented by continental “runoff” (mostly ice). Antarctic runoff amounts to nearly 8% of the global total from ~10% of the land surface. 20-25% of the freshwater input to the Southern Ocean is in the form of ice.

14. In the far south the deep water layer rises to a few hundred metres depth and can access the continental shelf. The increase in salinity on the continental shelves (as a result of sea ice formation and export) only partially offsets the freshening. Extreme cooling, resulting from interaction with floating ice (especially ice shelves), is the key to bottom water production.

15. Melting occurs beneath the ice shelves only because pressure lowers the freezing point. The product is Ice Shelf Water (ISW, T< -1.9°C). Dense waters flowing off the shelf form Antarctic Bottom Water. [Jacobs et al., JGR, 1985] Around most of Antarctica virtually all the ocean heat brought onto the continental shelf is lost to the atmosphere. The water is cooled to the surface freezing point (approx. -1.9°C) and subsequent growth of sea ice raises the salinity.

16. On the continental shelves of the Amundsen and Bellingshausen seas only the surface layer (top ~300 m) is close to the freezing point. CDW is present beneath this layer, with temperatures > +1°C. Almost unmodified CDW survives because either more CDW comes on shelf, or less sea ice forms, or both. Ice shelf melt rates are much higher and no ISW or AABW forms. [Hellmer et al., ARS, 1998]

17. (ii) Impact of melting ice on the ocean (a) Ice-salt-water system To understand what happens when ice and ocean meet we need only recall a few simple school science experiments. The equilibrium temperature of an ice- water mixture is the freezing point. Ice melts or forms until this temperature is attained. Increased pressure lowers the freezing point.

18. Seawater contains most of the elements on Earth. Its “salinity” is a measure of the overall ionic concentration (not just Na + Cl - ). For simplicity we consider a salt solution. Its “freezing point” is a function of concentration. At concentrations above the eutectic, “freezing” means precipitation of salt; below the eutectic it means precipitation of ice. Ice in seawater above the “freezing point” will melt (or dissolve) until cooling and dilution of the solution brings it to the “freezing point”.

19. The density of seawater is a complicated function of temperature, salinity and pressure. At a defined pressure (in this case atmospheric) we can plot contours of equal density on the phase diagram. Comparing the slope of the contours with the cooling/dilution caused by melting tells us whether upwelling or downwelling will result. In the polar oceans upwelling always occurs.

20. (b) The ice pump The freezing point of seawater decreases by 0.76°C for every 1000 m of depth in the ocean. Pressure (depth) changes will induce phase changes when the water is close to the freezing point. Atmospheric cooling cannot make the water colder than the surface freezing point, so waters flowing beneath an ice shelf always have the potential to melt.

21. Consider an insulated tank of water of uniform salinity, cooled at the surface to the freezing point. We introduce a vertical slab of ice. This can only coexist with the water at the surface. Below the surface the water is above the local freezing point. The ice melts, cooling and diluting the adjacent water.

22. The cooled water is now buoyant and rises to the surface. Here it is below the freezing point. Ice forms until the release of latent heat has warmed the water back to the surface freezing point. Equilibrium is reached when all the ice is at the surface. The “ice pump” requires no external input of energy. It lowers the PE of the system by moving the lower density ice to the surface.

23. Ross/Weddell SeaAmundsen/Bellingshausen Sea On a large scale this happens beneath the Antarctic ice shelves. Dense salty water, which forms beneath the sea ice, is transformed into buoyant Ice Shelf Water by melting. The rising ISW would rapidly freeze, but mixing with the inflowing water provides a continuous (but diminishing) supply of heat. As the temperature of the inflow rises above the surface freezing point, the region of freezing is moved upwards and eventually eliminated.

24. (iii) Circulation and melting beneath ice shelves (a) Ocean dynamics Ocean currents are governed by Newton’s second law of motion: This is valid only in an inertial reference frame. Transformation to an Earth-fixed, rotating reference frame introduces the Coriolis force. The components of the stress tensor are: These are the equations familiar to glaciologists, except: (i) we have retained the acceleration and Coriolis terms. (ii) the stress/strain relationship is linear.

25. Consider the scales of horizontal motion beneath an ice shelf: Horizontal length, L s ~ 10 5 m Depth, H s ~ 10 2 m Horizontal velocity, U s ~ 10 -1 m s -1 Rotation, Ω s ~ 10 -4 s -1 Time ~ L s /U s Forces arising from molecular viscosity (ν ~ 10 -6 m 2 s -1 ) are negligible. Turbulent viscosity is higher, but the viscous terms remain small. The acceleration term is generally negligible (Rossby number <<1). Both viscous and acceleration terms can become important where the velocity is high and/or the relevant length scale is small.

26. For vertical motion beneath ice shelves, other scales come into play: Gravity, g ~ 10 m s -2 Vertical velocity ~ U s H s /L s To a very good approximation the pressure gradient balances gravity: We can diagnose the pressure within the ocean directly from the density distribution, as if the water were at rest.

27. Horizontal flow is controlled (mainly) by the balance between the pressure gradient and the Coriolis acceleration: Such flow is called “geostrophic” (i.e. earth-turned). where 2Ω z =2Ωsin(Lat) and is normally denoted by f. From the geostrophic equations we see that fluid flows perpendicular to the pressure gradient and is non-divergent (if f is constant). Vertical differentiation of the equations gives: A homogeneous fluid is vertically rigid, but horizontal density gradients produce vertical shear.

28. At a solid boundary (ice shelf base or seabed) the velocity must tend to zero as a result of friction. We can estimate how close we must be to the boundary for friction and the Coriolis term to be of the same magnitude: For a typical eddy viscosity of 10 -2 the depth scale is 10 m. Within the frictional (Ekman) layer, drag reduces the velocity component perpendicular to the pressure gradient driving the flow. The balance between the Coriolis term and the pressure gradient is disrupted and the flow in the Ekman layer acquires a component down the pressure gradient (perpendicular to the geostrophic current).

29. The only direct forcing on the large-scale circulation beneath an ice shelf is the horizontal pressure gradient. Pressure gradients are generated by a slope in the sea surface or a slope of the density surfaces. A slope in the sea surface produces a pressure gradient, and hence a current, that is constant with depth. Sloping density surfaces produce a pressure gradient that varies with depth and hence a sheared current. (b) Circulation and melting

30. Beneath an ice shelf there is a large surface slope, but this is balanced by the pressure gradient imposed by the ice. Phase changes influence the density of the water near the ice shelf base and tilt the density surfaces away from the horizontal. We expect a sheared flow, predominantly in geostrophic balance, but with friction becoming important near the ice shelf and seabed. The motion promotes turbulent mixing, bringing heat up to the ice shelf base and sustaining the circulation.

31. The layer adjacent to the ice shelf base is a buoyant mixture of inflowing water and melt water. Right at the ice shelf base the water is at the freezing point. Heat is supplied to the mixed layer by turbulent entrainment: Turbulent heat transfer across the ice/ocean boundary layer drives the melting:

32. (c) Model results: idealised and real We consider first a simple sectoral domain (70-80S, 0-15E) with a flat seabed (at 1000 m depth) and an ice shelf in the south. There is no external forcing, but there is restoration to initial conditions at the northern boundary and at the surface (temperature set to the surface freezing point). The circulation is consistent with an ice pump, but the picture is complicated by the large horizontal scale and rapid rotation.

33. The mixed layer adjacent to the ice shelf base is cooled and freshened by melt. It flows up the ice shelf base, with a component to the left. Divergence along eastern and southern boundaries draws warm water up into the mixed layer. This sustains the rapid melting there. Freezing dominates in the west where the outflow is concentrated. Deeper waters are drawn under the ice shelf, bringing more heat into the cavity. The inflow is concentrated in the east

34. Next we consider the Filchner-Ronne Ice Shelf (FRIS). FRIS lies in the southern Weddell Sea, where the continental shelf is dominated by water at the surface freezing point, formed in winter. The patterns of melting and freezing are more complex, but the basic pattern is still visible. The differences arise because of the more complex geometry. [Joughin and Padman, GRL, 2003].

35. Rapid melting near the grounding line drives flow of the mixed layer up along the ice shelf base. The outflows follow western coasts, so this is where the freezing is concentrated.

36. Warm (-1.9°C) inflows drain into the deepest parts of the cavity, guided by the seabed topography. The seasonal production of dense shelf waters imposes an annual cycle on circulation and melting throughout most of the cavity.

37. (iv) Impacts of climate change (a) Sensitivity of melt rate to water temperature Now we return to our idealised ice shelf and restore the northern boundary to a range of different temperatures. We also try a range of different ice shelf and seabed shapes.

38. In each case the mean melt rate over the entire ice shelf base is a quadratic function of water temperature. But the actual function is dependent on geometry. Shorter, steeper ice shelves are more sensitive to temperature. Why quadratic? Recall that melting is proportional to the temperature and velocity in the mixed layer adjacent to the ice shelf base.

39. The mixed layer is simply inflowing (ambient) water modified by the addition of meltwater. Right at the ice shelf base the water is at the freezing point. In steady state there will be an overall balance between heat supplied by entrainment and consumed by melting: So: TfTf TDTD T

40. So (T-T f ) and (T D -T) both rise linearly with increasing T D. The linear increase in (T D -T) means a linear rise in (S D -S) and a near- linear rise in the density contrast between boundary layer and ambient. For a geostrophic current this means a linear rise in the velocity difference between boundary layer and ambient water. Melt depends on both velocity and (T-T f ), so the rise is quadratic (an inevitable result for a turbulent, buoyancy-driven, geostrophic flow).

41. (b) Forcing on shelf water temperatures Speer et al., 2001 Shelf waters are derived from upwelling CDW, which has relatively constant properities, unaffected by recent atmospheric change. On-shelf properties are determined by the supply of CDW and the degree to which it is modified. Around much of Antarctica shelf water properties are completely reset by surface freezing. The temperature is fixed at -1.9°C.

42. The Amundsen and Bellingshausen seas are different. Almost unmodified CDW survives on-shelf. There is a seasonal input of water to Pine Island Bay (at least in a model) driven by the local winds.

43. Variability in the wind forcing leads to variable amounts of deep water on shelf. There are minor changes in the deep water temperature, but major changes in the heat content of the water column. In the late ’80’s and early ’90’s little deep water was present.

44. Seasonal production of dense shelf waters fixes the inflow temperature at -1.9°C for the larger Antarctic ice shelves. Moderate climate warming might lead to a decrease in melting. But if CDW is present on-shelf the situation changes. Its temperature is fairly stable, but the supply of CDW to the shelf is controlled by ocean dynamics, in particular the wind forcing. The winds are driven by solar heating of the atmosphere. Ross/Weddell SeaAmundsen/Bellingshausen Sea

45. Summary I All ice discharged from Antarctica melts into the ocean, either from the base of ice shelves or from drifting icebergs. Wind-driven upwelling around Antarctica supplies water that is up to 3°C above the surface freezing point to the continental shelves. Around much of the coast heat loss beneath growing sea ice lowers the water temperature to -1.9°C. Melting occurs in all cases because pressure lowers the freezing point. This drives a buoyant outflow that is turbulent and nearly geostrophic.

46. Where the waters are cold, some refreezing occurs and the resulting “Ice Shelf Water” contributes to Antarctic Bottom Water formation. Where the waters are warm, melting is two orders of magnitude higher and no Ice Shelf Water forms. The melt rate is an ice-shelf-specific, quadratic function of inflow temperature. The ice shelves are more susceptible to changes in wind forcing, affecting the delivery of deep water to the shelf, than to changes in air temperature (unless high enough to cause surface melting). There is some evidence that the winds over the Southern Ocean could be changing as a result of anthropogenic influence on the atmosphere. Summary II