1. Modeling Antarctic RF attenuation By Amir Javaid University of Delaware

2. Topics Existing attenuation models Problems with the existing attenuation models Tasks for better attenuation models Steps toward better attenuation model Temperature profiles (high and low depth areas) Frequency, temperature and impurity dependent Attenuation Models Modeled attenuation profiles. (high and low depth areas)

3. Existing Attenuation models Attenuation models in icemc[1] Attenuation models in SAM. Siple Dome and Lake Vostok RF attenuation models from Joseph. A. Macgregor's Thesis attenuation models[2].

4. Icemc Attenuation Models There are two kind of attenuation models used in icemc. Constant Attenuation Lenght(L=700m) Variable Attenuation Length There are three types of model for variable attenuation length depending upon the GPS position of the event. Ross & Ronne Ice shelves attenuation model West land attenuation model Ice sheets attenuation model

5. Icemc Attenuation Models Ross & Ronne Ice shelves attenuation model For Ice Shelves, Ronne Iceshelf is treated in the same way as Ross Ice Shelf.The average attenuation length for upward direct rays is calculated by the following formula. For reflected rays which are first downward and then upward, the average attenuation length is calculated by where the interaction performed from the height of the interaction relative to the surface x = (a negative number) to the surface (x = 0). Since the measurements were only carried outto a depth of 420 m at Ross Ice Shelf, an effective maximum depth and effective interaction depth are utilized given by

6. Icemc Attenuation Models Ice Sheet attenuation model For direct rays the average attenuation length is calculated by and for the reflect rays Here the measurements were only carried out to a depth of 2810 m, so In the above formulas,d max is the real maximum depth of the ice at the longitude and latitude position where the event has occurred. d int is depth of the interaction (a positive number)

7. Comparison between Attenuation models in SAM and icemc The Ice Sheet and Ross ice shelf models in the figure below are from icemc and the 0.4,0.8 and 1.2GHz models are from SAM based on the South Pole temperature profile.

8. Joseph Macgregor's Thesis attenuation models Attenuation Model formulas. Data used for Siple Dome attenuation model. Attenuation Rates for Siple Dome. Attenuation Rates for Lake Vostok.

9. Attenuation Model Formulas MacGregor has used the following equation to measure attenuation length where is the pure ice conductivity, H and u ssCl- are molar conductivities, E pure, E H+ and E ss Cl- are activation energies, k is Boltzmann's constant, T is temperature in Kelvin and T r = 251 K is a reference temperature. The ionic concentrations [H + ] and [ssCl - ] are measured in molL -1. The molar conductivities are measured in Sm -1 M -1. Where S is Siemens which has units of 1/Ohm.

10. Data used for Siple Dome attenuation model References [2] Joe Macgregor's PhD thesis

11. Data used for Siple Dome attenuation model (contd..) References for above table [2] Joe Macgregor's PhD thesis

12. Attenuation Rate for Siple Dome Using the chemical and Temperature data for Siple Dome the attenuation rate values for Siple Dome are given in the figure below. References [2] Joe Macgregor's PhD thesis

13. Attenuation Rate for Lake Vostok References [2] Joe Macgregor's PhD thesis

14. Problems with the existing models Too few models. May not represent the attenuation profile over the whole Antarctica. Most of these models do not include frequency dependence. Impurity dependence is also missing in some of these models.

15. Tasks for a better attenuation model A better attenuation model of Antarctica for ANITA require the following task. Modeling of temperature profile throughout the region in Antarctica which was under the horizon of ANITA1 and ANITA2. To perform this task temperature profiles from different parts of Antarctica are required. Modeling of conductivity and permittivity for Antarctica. This task needs impurity data for antarctic ice. Testing the models for the ANITA frequency band.

16. Steps towards Antarctic RF Attenuation Modelling Collect the existing data sets for temperature profiles and chemical concentration parameters needed which include the molar conductivities and acid concentrations for different parts of Antarctica. Divide the Antarctica in patches with similar temperature and chemical concentration. Find out how the temperature and chemical concentration can be interpolated throughout the patch. This means finding the reasons for their existing temperature and chemical composition. The conductivity and attenuation length formulas defined before can be used to calculate attenuation. Correct the attenuation models for higher frequencies.

17. Steps towards better Antarctic RF Attenuation Model As a first step to model the RF attenuation, I have collected a set of temperature profiles from the following 13 different places in Antarctica. Most of these data sets are taken from the book “The physics of glaciers” by W.S.B Paterson. South Pole Vostok station Siple Dome Felchner(Ronne ice shelf) Byrd9 station Ross j9 station Ross (Little America) Mt Fuji Ice stream B Amery Mirny Maudheim Law Dome Collection of impurity concentration data sets in under progress.

18. Temperature profiles(low Depth places) References [3] “The Physics of glaciers” W.S.B Paterson

19. Temperature profiles( high depth places) References [2] Joe Macgregor's PhD thesis References [4] Vostok station temperature profile[7]

20. Frequency, Temperature and Impurity dependent Attenuation Models Fujita et al and J. A Dowdeswell et al have developed attenuation models for ice which are impurity, temperature and frequency dependent. I have utilized the model developed by Fujita et al to model the attenuation for different parts of Antarctica. The model plots are shown below. References for above plots [5] [6]

21. Data for the pure and impurity based attenuation models The data used to produced the pure and impure ice attenuation plots in the previous slide is shown in tables 1, 2 and 3. For pure ice the conductivity can be written as The complex permittivity for pure ice can be modeled as follows The parameters A, B and C are given in table 1. For impure ice the real part of permittivity is modeled by experimental measurement. The parameterization formula can be written as follows The formula for conductivity for impure ice is similar to the one for pure except there is molar concentration multiplier at the end.

22. Modeled Attenuation Profiles(High depth areas)

24. Attenuation Profiles(low depth places)

25. Modeled Attenuation Profiles(Low depth areas)

26. South Pole attenuation model comparison

27. Ross Ice Shelf attenuation model comparison

28. To do list More temperature and impurity concentration profiles are needed. Study the spatial variation of temperature and impurity concentration. Investigate the correlation of temperature and impurity profiles for different parts of Antarctica type of ice, age of ice,thickness and distance from the sea.

29. References (1) Amy Connolly, David Saltzberg “Summary of a Simulation of the ANITA Detector” August 13, 2008. (2) Joseph A MacGregor “Development and Applications of a Radar-Attenuation Model for Polar Ice Sheets”, PhD thesis 2008 University of Washington. (3) “The Physics of glaciers” W.S.B Paterson Pergamon (1994) (4) Yoshiyuki Fujii et. al Mem. Natl. Inst. Polar Res Spec ． lssue 、 56 ， 103 － 116 ， (2002) (5) Fujita et.al Physics of Ice Core Records: 185-212 (2000) (6) J. A. Dowdeswell and S. Evans Rep. Prog. Phys. 67, 1821-1861 (2004) (7) I. A Zotikov “The thermophysics of glaciers”. (1986)