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Inferring Transients inIce Flow, Ice-Sheet Thickness,
and Accumulation Ratefrom Internal Layers
(near the WAIS Divide ice-core site)
Michelle Koutnik, Ed Waddington, Howard Conway University of Washington
Tom Neumann NASA
Steve Price Los Alamos National Laboratory
How do we infer histories of accumulation and ice dynamics from internal layers?
How well can we infer histories of accumulation and ice dynamics from internal layers?
How do we infer histories of accumulation and ice flow from internal layers?
Estimate unknowns (e.g. accumulation-rate history)
How do we infer histories of accumulation and ice flow from internal layers?
Estimate unknowns (e.g. accumulation-rate history)
Track particlesthrough transient
velocity field
Generateinternallayers
How do we infer histories of accumulation and ice flow from internal layers?
Estimate unknowns (e.g. accumulation-rate history)
Track particlesthrough transient
velocity field
Generateinternallayers
Compare modeled observables to measured quantities; update parameters
iterate.
DATA SET (known)
• Internal layers
• Layer ages
• Modern ice velocity (from GPS)
• Geometry
• Accumulation rates at any point and time
DATA SET (known)
• Internal layers
• Layer ages
• Modern ice velocity (from GPS)
• Geometry
• Accumulation rates at any point and time
PARAMETER SET (unknown)
• Accumulation rate (x,t)
• External-flux forcing (xbounds,t)
• Ice thickness (x0,t0)
• Layer ages
• Ice flux into solution domain (x0,t0)
• Temperature-independent ice softness
• Geothermal flux
FORWARD ALGORITHM
2.5-D thermomechanical ice-flow model.
• Ice-surface evolution
• Ice-temperature evolution
• Ice-velocity field
Track particles to map out an internal layer.
FORWARD ALGORITHM
2.5-D thermomechanical ice-flow model.
• Ice-surface evolution
• Ice-temperature evolution
• Ice-velocity field
Track particles to map out an internal layer.
INVERSE ALGORITHM
Use a gradient inverse method.
• Regularized problem:
• Fit data within a tolerance
• Smooth accumulation profile
• Linearized problem
Find updates to parameter estimates.
“There may be no model that exactly fits the data.”
“If exact solutions exist, they may not be unique…”
“The process of computing an inverse solution can be, and often is, extremely unstable in that a small change in measurement can lead to an enormous change in the estimated model.”
(Aster et al. 2005, pg. 12)
pN
kk
k
iii p
p
rrr
1
0
Linearized problem
)Tν(+=I p222 dp
pN
kk
k
iii p
p
ccc
1
0
Model size Model residuals
How well can we infer histories of accumulation and ice flow from internal layers?
• Accumulation rate (x,t)
• External-flux forcing (xbounds,t)
• Ice thickness (x0,t0)
• Layer ages
• Ice flux into solution domain (x0,t0)
• Temperature-independent ice softness
• Geothermal flux
magenta = initial guessgrey = actual (known) solutionblue = inferred solutionblack = inferred with accumulation rates through time
magenta = initial guessgrey = actual (known) solutionblue = inferred solutionblack = inferred with accumulation rates through time
Preliminary results:
- Internal layers can be used to infer:
accumulation-rate history ice-thickness (ice divide) history
externally forced flux history
- There may be some tradeoff between parameters, but accumulation rates through time may provide rate control
- Requiring a spatially smooth accumulation history can sufficiently regularize this inverse problem
Near WAIS Divide ice-core site:
- Extend spatial and temporal histories beyond the Holocene
- Use layers dated from the ice core