[CM2015] Chapter 9 - Land Ice Modeling
Transcript of [CM2015] Chapter 9 - Land Ice Modeling
Chapter 9Land Ice, Climate, and Modeling
Yonggang Liu
William M. Connolley
Lisiecki and Raymo (2005, Paleoceanography)
Petit et al. (1999, Nature)Figure by Robert A. Rohde
Land Ice Sheet Drew Tremendous Attention During the Past Decade
Paolo et al. (2015, Science) NOAA Arctic Report Card for 2013
How Does Ice Sheet Affect the Climate?
Answer: mainly through albedo feedback
But sea level rise has a substantial impact on the human society
What Property of the Ice Sheet Do We Care About the Most?
Answer: its mass or thickness
Where h is the thickness of ice sheet, A dot and B dot are the surface and basal mass balance, respectively, q = uh is the mass flux
Surface and Basal Mass Balance
Winkelmann et al. (2012, Nature)
Dynamics (to get mass flux q)
Deviatoric stress
Strain rate
Pressure
Constitutional relationship
where
Stokes’ Equations
What’s the difference from themomentum equation for theatmosphere and ocean
T’ is a tensor, which makes the Stokes’ Equation hard to solve
Are all these components important for the ice sheet?
http://mail.colonial.net/~hkaiter/Glaciers_Ice_Ages.html
Ice sheet is very thin compared to its horizontal scale; It is moving slowly
Winkelmann et al. (2012, Nature)
Additionally, in most part of the ice sheet, vertical shear dominates the motion
Shallow-Ice Approximation
Where s and b are surface and bottom elevation, respectively. C(T) is the basalsliding constant and B dot is the basal melting rate.
Then we get decoupled equations of u, v and w (Greve, 1995)
, andAssume
Note the temperature dependence
Alpine Glacier (http://mail.colonial.net/~hkaiter/Glaciers_Ice_Ages.html)
Lateral friction is large, obviously cannot ignored
Other examples: fast flowing ice streams
Full Stokes’ Equation needs to be solved!
Shallow-Shelf Approximation
Assume vertical shear is 0
Winkelmann et al. (2012, Nature)
The following equations result
Thermal dynamics
What assumption has been made?
Boundary conditions
T = Ta
Q = Qb At the bottom
At the surface
The viscosity of ice is dependent on temperature, and frictional heating andgeothermal heating at the bottom of the ice sheet may cause melting there.These require that the temperature evolution of the ice sheet need to besolved.
Where
is the frictional heating
MacAyeal (1997)
Summary