1. Thermodynamics of ice Karthaus 2005-09-15 Why is temperature so important? Stores memory of past climate changes Deformation rate of ice depends on the temperature of the ice Basal melting and basal erosion depends on basal temperature Velocity of seismic and radar waves depends on temperatur and water in ice

2. Heat equation for beginners: Heat flux Q (heat flowing across a unit area in unit time) is proportional to the temperature gradient  T/  z Q = -K  T/  z 0 deg C-50 deg C KThermal conductivity [Wm-1K-1]2.102.76 CSpecific heat capacity [Jkg-1K-1]20971741  Thermal diffusivity [m2s-1]1.09 10-61.73 10-6 LLatent heat [kJkg-1]333.5

4. The full equation

5. 6  2 T  z 2 = w  T  z w = -bz/h

6.  T  t =  (   T  z )  z+  2T  z2 - w  T  z - u  T  x + f/(  c)

8. Boundary conditions: Surface: T(z=H,t)=Tsur(t) Bed:  T/  z = -G/K if there is no basal melt T(z=0) = Tmelt if there is basal melt  Lbmelt = G + Qf +K  T/  z

9. Logging at NorthGRIP, 2000 Niels Gundestrup

10. GRIP Dye3

12. Paleaotemperatures from borehole measurements Data: Measurement of the present temperature in a bore hole. 50m intevals are used (61 observations) What are the model parameters?

13. d=G(m) - non linear Divide the time into 125 intevals. The inteval lengths are chosen so they reflect the resolution/diffusion of the problem Model parameters: 125 temperatures + Qgeo

24. Deep Ice Cores in Antarctica ProjectYearDepth Byrd68-702164 m Vostok79-(3623 m) DomeF95-962500 m 04-(925 m) EPICA DC97-053265 m EPICA DML 01 -(2650 m) EPICA DC VOSTOK DOME FUJI EPICA DML Byrd Law Dome

25. Law Dome, DSS deep ice core Liquid filled borehole Length 1200 m Drilling terminated in 1993 Borehole temperatures measured in 1996 Resolution 0.02 K (Morgan et al., 97, JoG)