Effects of firn on determining bed topography of polar ice sheets using

radar

Kenny Matsuoka1,Stefan Ligtenberg2, Michiel Van den Broeke2

1. Norwegian Polar Institute2. 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 Institute2. IMAU, Utrecht University

Radio-wave propagation speed

Air in the Antarctic ice

Van den Broeke (2008, Antarctic Science)

40 m

30 m

20 m

10 m

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

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.

Ice thickness estimate using radar12

H 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

cvn

cvn

0

Hn z dz

nH

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)

Frequently-used relationships

Depth profiles of density

2f

Surf i i f2f

i f

z zz z

H z

z z

Equation 9.81 in Greve and Blatter (2009, Dynamics of ice sheets and glaciers)

surf: 400, 450, 500, 550 kg/m3.

hf : 60, 80, 100 m

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 (surf, hf) = (400 kg/m3, 100 m)

and smallest when (600 kg/m3, 60 m).

•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)

Which n 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.

Depth-averaged <v>

vi = 168.5 m/ms

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 i12

H v T

ii 0

i

12

v vH v v T H

v

D

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

Firn correction DH variations

DH is virtually independent of ice

thickness.

vi = 168.5 m/ms

DH for ice shelves

DH is virtually independent of ice

thickness.

vi = 168.5 m/ms

DH for the Antarctic Ice Sheet

Input data: Fretwell et al. (2013, TC) and Ligtenberg et al., (2011, TC)

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

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.