effects of firn on determining bed topography of polar ice sheets using radar kenny matsuoka 1,...
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![Page 1: Effects of firn on determining bed topography of polar ice sheets using radar Kenny Matsuoka 1, Stefan Ligtenberg 2, Michiel Van den Broeke 2 1.Norwegian](https://reader036.vdocument.in/reader036/viewer/2022081519/56649cf95503460f949cab70/html5/thumbnails/1.jpg)
Effects of firn on determining bed topography of polar ice sheets using
radar
Kenny Matsuoka1,
Stefan Ligtenberg2, Michiel Van den Broeke2
1. Norwegian Polar Institute
2. IMAU, Utrecht University
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Effects of firn on determining bed topography of polar ice sheets using
radar
Kenny Matsuoka1,
Stefan Ligtenberg2, Michiel Van den Broeke2
1. Norwegian Polar Institute
2. IMAU, Utrecht University
![Page 6: Effects of firn on determining bed topography of polar ice sheets using radar Kenny Matsuoka 1, Stefan Ligtenberg 2, Michiel Van den Broeke 2 1.Norwegian](https://reader036.vdocument.in/reader036/viewer/2022081519/56649cf95503460f949cab70/html5/thumbnails/6.jpg)
Radio-wave propagation speed
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Air in the Antarctic ice
Van den Broeke (2008, Antarctic Science)
40 m
30 m
20 m
10 m
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Firn correction
“The majority of direct ice thickness measurements from radar and seismic
techniques were calculated with the inclusion of a “firn correction”.”
“ Routinely for radar measurements on thick ice, 10 m of additional ice thickness has
been added by researchers to account for the low-density/high-velocity firn layers.”
Fretwell et al. (2013, TC) BEDMAP2 group paper
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Is it a matter?
• Accuracy of ice thickness and ice mass in polar regions
• Data compilations• Errors in freeboard elevations of the ice
shelves and eventually estimates of marine ice thickness
• Errors in subglacial hydraulic potentials Individual researchers have made best estimates
for specific studies,but there is no continent-wide knowledge base.
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Ice thickness estimate using radar
1
2H v T
H : Ice thickness
<v>: Depth-averaged propagation speed
T : Two-way travel time
v : Local propagation speed
c : Propagation speed in vacuum
n : Refraction index
<n>: Depth-averaged n
cv
n
cv
n
0
Hn z dz
nH
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Estimating depth-averaged <v>
1.Pick a reasonable relationship between density and propagation speed.
2.Assume approximate depth profiles of density3.Using 1 & 2, estimate depth-averaged
propagation speed
Pure-ice propagation speed vi = 168.5 m/ms (ni = 1.78)
- Range of vi = 168 – 169.5 m/ms- Function of ice temperature, fabrics, and chemisty (e.g. Fujita et al., 2000)
Fujita et al. (2000, Physics of ice core reocrds)
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Frequently-used relationships
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Depth profiles of density
2
fSurf i i f2
f
i f
z zz z
H z
z z
Equation 9.81 in Greve and Blatter (2009, Dynamics of ice sheets and glaciers)
rsurf: 400, 450, 500, 550 kg/m3.
hf : 60, 80, 100 m
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Depth-averaged speed <v>CRIM Looyenga Kovacs Frolov
Red: firn thickness hf = 100 m; Green: hf = 80 m; Blue: hf = 60 m
Regardless of the refraction index models,<v> is largest when (rsurf, hf) = (400 kg/m3, 100 m)
and smallest when (600 kg/m3, 60 m).
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•Variations between models: ± 0.64 m/msIndependent of ice thickness and choice of densification parameters•Variations in pure ice: ± 0.75 m/msDependent on icetemperature andfabrics(Fujita et al., 2000)
Source of refraction-index uncertainty
Red: (400 kg/m3, 100 m)Blue: (600 kg/m3, 60 m)
Fujita et al. (2000, Physics of ice core reocrds)
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Which n -r relationship is best?
• Estimated propagation speeds depend minimal on the choice of the density/refraction-index relationship.
• So, use the simplest, linear equation, CLIM.
a in n A n I
Now <v> can be derived from air and ice thicknesses.We don’t need depth variations of the density.
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Depth-averaged <v>
vi = 168.5 m/ms
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Firn correction DH
• The first guess of the ice thickness H0 can be derived using pure-ice value of the depth-averaged propagation speed vi
• The best estimate of the ice thickness can be H0+DH, using firn correction DH:
0 i
1
2H v T
ii 0
i
1
2
v vH v v T H
v
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DH is usually assumed to be 10 m
“ Routinely for radar measurements on thick ice, 10 m of additional ice thickness has been added by researchers to account for the low-density/high-velocity firn layers.”
Fretwell et al. (2013, TC) BEDMAP2 group paper
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Firn correction DH variations
DH is virtually independent of ice
thickness.
vi = 168.5 m/ms
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DH for ice shelves
DH is virtually independent of ice
thickness.
vi = 168.5 m/ms
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DH for the Antarctic Ice Sheet
Input data: Fretwell et al. (2013, TC) and Ligtenberg et al., (2011, TC)
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Properties in the modeled DH
• Mean value: 9.2 m.• Inland Antarctica
– ~15 m
• Large (Ross, Ronne/Filchner) ice shelves– 8 -10 m
• Small ice shelves in Dronning Maud Land– < 5 m
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Take-home messages
• Firn correction values are virtually independent of ice thickness but gradually vary with air column thickness.
• Firn correction values are < 5 m in the DML ice shelves and 15-20 m in the inland EAIS.
• Please, show pure-ice propagation speed vi and firn correction DH in your paper.
• Please, consider submitting two-way travel time “data” together with ice thickness “estimates” to a world data center.