Ice in the climate system. Summary so far. Today. The Cryosphere. 1. Climate history of the Earth. 2. Paleo observations (1)

Transcription

1 Ice in the climate system 1. Climate history of the Earth 2. Paleo observations (1) 3. Paleo observations (2) 4. Ice ages 5. Climate sensitivity 6. Ice in the climate system Summary so far Radiation (Milankovitch theory) must be important Internal Feedbacks must be important (100 kyr) Interpretation sea level difficult earth response gravitational effects 7. Climate Change (2105) 8. Sea level (0406) Today What is the cryosphere? What are the basic features and terminology? How do climate and ice sheets interact? Basic physics of ice flow The Cryosphere Ice sheets (Antarctica and Greenland) Large topogrophy covering ice Ice shelves Floating (sweet, thick, permanent) Glaciers Land based ice in mountains Sea ice Frozen ocean water (salt, thin, semi permanent) Snow % NH covered with snow in winter Permafrost Frozen ground

2 Basic terminology Ice Sheet and Mass Balance Equilibrium line accumulation ablation calving flow lines ice core MASS BALANCE Accumulation = Ablation + Calving Differences Antarctica and Greenland, Glaciers!!!Antarctica!Greenland!Glaciers Accumulation!100%!!100%!!100%! Ablation!!0%!!50%!!80%!! Calving!!100%!!50%!!20%! Characteristics of the cryosphere Present day estimate of: Antarctic ice sheet (incl. ice shelves) Greenland Glaciers Area (10 6 km 2 ) Mean thickness (m) Volume (10 6 km 3 ) Sea level equivalent (m) Accumulation (10 (m 12 w.e. kg yr -1 ) ± ± Runoff (10 12 kg yr -1 ) ± Ice berg discharge (10 12 kg yr -1 ) Ice shelf basal melt (10 12 kg yr -1 ) ± ± ± ± 3 - Church et al., 2001

3 Time scales Ice and sea level time scales Snow cover: days-months Sea ice: months-10 years Glaciers: years Ice shelves: years Ice sheets: years Miller et al. 2005! Albedo feedback Albedo feedback Temperature lower Temperature higher Absorption less Snow/Ice more Absorption more Snow/Ice less Albedo higher Albedo lower

4 Hysteresis Ice leads to nonlinear response in the climate Forcing Ice volume Amplitude Linear Nonlinear Temperature Time R. Bintanja Cryospheric Feedbacks Response ice to climate change Change in annual temperature ( C) J. Oerlemans! (mwe/a) Antarctica Greenland annual temperature ( C) glaciers and small ice caps ablation accumulation spec. balance

5 Mass balance and climate change Modelling ice flow 0 Elevation Mass Balance (m/yr) Steady state Flow on a sloping surface "H "t = 0 M b = # b dxdy = 0 -Ice thickness remains constant everywhere -specific balance varies along the glacier/ice sheet, but is constant in time Shear stress: " xz = #gh dh s dx

6 Shallow ice approximation U=f(H,dH/dx)! Mass balance height feedback implicit! No thermodynamics! No bedrock compensation! Non-linear diffusion equation! Reference profile Rhone Altitude (m a.s.l.) modelled - observed Distance from head (km) Difference (m) Time evolution Rhone Future changes Rhone Green observed! Length (km) Length Volume ELA Year AD Volume (km 3 ) and ELA (km a.s.l.) Length (km) C +2 C 4 +2 C en +20% +4 C Time (AD)

7 Schematic flow (1) Schematic flow (2) Velocity m/yr! Flow mechanisms Major source of complications Temperature - flow parameter -hypsometry -time scale of the response basal melt Flow parameter (Pa -3 a -1 ) !T=10 >A'=10A!T=10 > A'=3A Temperature (K)

8 Importance -Deformation rate temperature dependent! -Criteria for Basal sliding! First Law of Thermodynamics:!!Internal Energy= Work done +!Heat Added!!!dE/dt!=!dW/dt!+! dq/dt!!!1!!2!!!3! Purpose now to rewrite this as a change in temperature over time! 1: Change of internal energy de dt = d"e = " de dt dt + e d" dt e!specific internal energy =c p T! c p!specific heat capacity!!!density (constant)! de dt = "C dt p dt 2:Work done deformation phase change W d = " ij # ij " ij strain rate # ij stress W l = L f M f L f Latent heat of fusion M f amount that refreezes 3: Heat added~conduction r F c = "k#t k thermal conductivity... (flux $ unit volume) dq dt = k#2 T

9 Combining the three terms dt "C p dt = k#2 T + $ ij % ij + L f M f writing the total derivative as sum of the local time change and advection! "T "t = #u"t "x # v"t "y # w"t "z + (advection) K "2 T "x 2 + K "2 T "y 2 + K "2 T "z 2 + (conduction) 1 ( % xx & xx + % yy & yy + % zz & zz )+ (internal deformation) $C p 1 (2 % xy & xy + 2 % xz & xz + 2 % yz & yz )+ $C p L f M f $C p (melt) Table of thermal parameters Thermal parameters of glacier ice (Paterson 1994) T 0 C T -50 C Specific heat C p 2091 Jkg -1 K Latent heat of fusion L f kjkg -1 Thermal conductivity k 2.1 Wm -1 K Wm -1 K -1 Thermal diffusivity K m 2 s m 2 s m 2 yr -1 Density! 917 kg m -3 Robin solution Assumptions! -The basal temperature is below pressure melting point.! -Horizontal diffusion is neglected compared to the vertical diffusion.! -Horizontal advection is neglected.! -Frictional heat from internal deformation is included in! the geothermal heat flux! valid at ice divide! "T "t = K "2 T "z 2 # w"t "z -steady state! -mechanical steady state > w known as function of z! Depth below the surface (m) Effect of vertical velocity ablation area T s =T melt T(z) - Ts ( C) M in cm/yr

10 T b -T s for M =10 cm /yr Vertical profiles Ice isolates Large G leads to melt at bottom Mind Hor. Advection Purple More or less ELA Temperature difference J. v.d. Berg Milankovitch phasing kyr transition (Ruddiman, 2000)

11 Transition kyr 100 kyr evolution of NAM ~1 m/1000 yr merging ~0.2 m/1000 yr Blue bar is first minimum after 100 ky interglacial (black arrow) Orange line connects max ice volume in 100 ky cycle BW08 Terminations Leads and Lags in the system Thermodynamics play role In kyr transition BW08

12 Summary Thermodynamics Central parts of ice sheets!!cold at the top warm near the bed!!vertical advection:!!! cools isothermal near the surface (~15 m)!!vertical diffusion:!!!redistributes geothermal heat!!!linear temperature profile near the bottom!!(robin solution)! Summary Thermodynamics (2) Downstream of the divide!!horizontal advection start to play a role!!particularly near the bed where deformation is largest!!-melt water penetration can be an important term!!-in addition deformation is strongly dependent on!!temperature!!simultaneous numerical solution of temperature and velocity! Summary Ice Flow Simple model: -shear stress driven models -isothermal Slightly more complicated: -short outline thermodynamics Summary ice in the climate Cryosphere important: as part of the climate system (passive and active) as climate archive for sea level Basic terminology: Ice sheet, shelves, glaciers, sea ice Mass balance, accumulation, ablation, equilibrium line Difference mass balance Antarctica, Greenland, glaciers Relation mass balance and flow Perfect plasticity

13 Further reading *W.S.B. Paterson The Physics of Glaciers *J. Oerlemans Glaciers and climate change *C. Van der Veen Fundamentals of Glacier Dynamics *R. Leb. Hooke Principles of Glacier Mechanics