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 Polar Institute 2.IMAU, Utrecht University

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5. 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 Polar Institute 2.IMAU, Utrecht University

6. Radio-wave propagation speed

7. Air in the Antarctic ice Van den Broeke (2008, Antarctic Science) 40 m 30 m 20 m 10 m

8. 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

9. 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.

10. Ice thickness estimate using radar H : Ice thickness : Depth-averaged propagation speed T : Two-way travel time v : Local propagation speed c : Propagation speed in vacuum n : Refraction index : Depth-averaged n

11. Estimating depth-averaged 1.Pick a reasonable relationship between density and propagation speed. 2.Assume approximate depth profiles of density 3.Using 1 & 2, estimate depth-averaged propagation speed Pure-ice propagation speed v i = 168.5 m/  s ( n i = 1.78) - Range of v i = 168 – 169.5 m/  s - Function of ice temperature, fabrics, and chemisty (e.g. Fujita et al., 2000) Fujita et al. (2000, Physics of ice core reocrds)

12. Frequently-used relationships

13. Depth profiles of density Equation 9.81 in Greve and Blatter (2009, Dynamics of ice sheets and glaciers)  surf : 400, 450, 500, 550 kg/m 3. h f : 60, 80, 100 m

14. Depth-averaged speed CRIM Looyenga KovacsFrolov Red: firn thickness h f = 100 m; Green: h f = 80 m; Blue: h f = 60 m Regardless of the refraction index models, is largest when (  surf, h f ) = (400 kg/m 3, 100 m) and smallest when (600 kg/m 3, 60 m).

15. Variations between models: ± 0.64 m/  s Independent of ice thickness and choice of densification parameters Variations in pure ice: ± 0.75 m/  s Dependent on ice temperature and fabrics (Fujita et al., 2000) Source of refraction-index uncertainty Red: (400 kg/m 3, 100 m) Blue: (600 kg/m 3, 60 m) Fujita et al. (2000, Physics of ice core reocrds)

16. 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. Now can be derived from air and ice thicknesses. We don’t need depth variations of the density.

17. Depth-averaged v i = 168.5 m/  s

18. Firn correction  H The first guess of the ice thickness H 0 can be derived using pure-ice value of the depth-averaged propagation speed v i The best estimate of the ice thickness can be H 0 +  H, using firn correction  H :

19.  H 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

20. Firn correction  H variations  H is virtually independent of ice thickness. v i = 168.5 m/  s

21.  H for ice shelves  H is virtually independent of ice thickness. v i = 168.5 m/  s

22.  H for the Antarctic Ice Sheet Input data: Fretwell et al. (2013, TC) and Ligtenberg et al., (2011, TC)

23. Properties in the modeled H 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

24. 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 v i and firn correction  H in your paper. Please, consider submitting two-way travel time “data” together with ice thickness “estimates” to a world data center.

25. v i for pure ice Fujita et al. (2000) in Physics of Ice Core Records

26. Alternatively, larger can be used = 170 m/  s, 0.5 m/  s larger than the pure-ice value It’s a bad idea, as depends both on ice and air thicknesses.

27. Tune v i together with  H ? It’s really a bad idea, as  H depends both on ice and air thicknesses. v i = 168 m/  s v i = 168.5 m/  s