December 13th, 2010 Thomas Phillips, Harihar Rajaram and Konrad Steffen

1. The influence of cryo-hydrologic warming on the ice temperature in the ablation zone – insights from a computational model December 13th, 2010 Thomas Phillips, HariharRajaram and Konrad Steffen University of Colorado

2. Cryo-Hydrologic System • Cryo-Hydrologic System [krī ʹō hī drol ʹə gėc sis ʹtəm]: describes the water channel network in the ablation zone of a glacier. The melt water generated at the surface flows through the network to the base of the ice sheet and the margin where it leaves the ice. Intro Fuzzy Logic Model Dual Column Model Flowline Model CSP Model

3. Dual Column Equations ICE COLUME EQUATION The Budd (1969) column model for englacial temperaturs: Θ_ice Θ_m Transient conduction Horiz. Adv. Vertical . Adv. Shear heating Cryo-Hydrologic Heat Exchange Term The modified ice column in this model: This term is used to simulate the interaction of the Ice column with nearby conduits Intro Dual Column Model Flowline Model

4. Dual Column model results The initial ice temperature has No influence on the new steady State temperature. The increase in temperature results in an increase in an increase in the flow parameter A and in the observed velocity. • The value of R influences the temperature in • Two respects: • The length of time necessary to reach a new • Steady state: Small R = short transition period • 2) The new steady state temperature: small R [W/K/m] = higher • New steady state temperature. Phillips et al. 2010 Intro Fuzzy Logic Model Dual Column Model Flowline Model CSP Model

5. Model Setup • Greenland Central Ridge: Conventional Budd Column model • Surface Boundary conditions: mean annual air temperature but not to exceed 273.14 K (melting point). • Basal Boundary conditions: geothermal heat flux; not to exceed the pressure melting point. • Iterations: From first column in flow direction. Each column is iterated so that hor. Vel, A andd temp are in agreemment. Intro Fuzzy Logic Model Dual Column Model Flowline Model CSP Model

6. Climate Change in Greenland: The melt area for Green- land is showing an increas- ing trend. On average Greenland is currently los- ing 220 km3 yr-1 (Hanna et al. Journal of Climate, 2008) Flowline Intro Fuzzy Logic Model Dual Column Model Flowline Model CSP Model

7. Steady State Flow Model • The changes in ice temperatures in the accumulation zone are in millennia. Hence there is little change to be expected within a century. • The changes in temperature assumed in this study is within decades. This is a fraction of the time steps used in models to simulate changes on an ice sheet.

8. Temperature Profiles 2008

9. Temperature Increase Results Three runs were performed to calculate the difference influence of englacial water on the ice temperature of the ablation zone of the Sermeq Avannarleq glacier in Greenland: Top: The difference of having cryo-hydrologic warming on and off for 2008. The equilibrium line is at 1250 meters Notice there are two hotspots: Near the surface due to englacial water flow. The second at the bed due to the fact that water reaches the bed. The lower image shows the increase between 2008 and 1990. k/R^2 is [ W/K/m] Intro Fuzzy Logic Model Dual Column Model Flowline Model CSP Model

10. Temperate Ice at the Bed Left: The temperate bed moves inland due to the increased melt between 1990 and 2008. The cryo-hydrologic term ensures that the bed becomes temperate further inland (right)

11. Temperature comparison at bore holes Cyan: no cryo-hydrologic warming, magenta: cryo hydrologic warming. Offset in left figure: the ice thickness is underestimated in the model.

12. Influence on the viscosity and velocity Top right: velocity profile for 2008 Max. surface 145m/a, bed: 6m/a Bottom right: velocity increase between 1990 and 2008. Top Right: Factor of increase of the Glen’s flow law parameter A=[1/Pa3/a] .

13. Questions