Modeling Antarctic RF attenuation By Amir Javaid University of Delaware

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) Conductivity calculation(pure and impure ice) Attenuation length calculation Modeled attenuation profiles. (high and low depth areas) South Pole attenuation model comparison Ross ice shelf attenuation model comparison To do list References

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].

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

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

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)

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.

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.

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.

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

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

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

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

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.

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.

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.

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 (Latitude=-90) Vostok station (Latitude =78.5 S,Longitude=106.8E) Siple Dome (Latitude =75.9 S,Longitude=83.9E) Felchner ice shelf (Latitude =79.61 S,Longitude=46.72E) Byrd9 station (Latitude =80 S,Longitude=120W) Ross j9 station (Latitude =82.4 S,Longitude=168.6W) Ross (Little America)(Latitude =78.2 S,Longitude=162.2W) Dome Fuji (Latitude =84 S,Longitude=145W) Ice stream B(Whillians ice stream) (Latitude =80 S,Longitude=120W) Amery (Latitude =70.9 S,Longitude=69.9E) Mirny (Latitude =62.5 S,Longitude=114E) Maudheim (Latitude =71.1 S,Longitude=10.9W) Law Dome (Latitude =66.2 S,Longitude=110W) Collection of impurity concentration data sets in under progress.

Temperature profiles References [3] “The Physics of glaciers” W.S.B Paterson

Temperature profiles References [2] Joe Macgregor's PhD thesis References [4] Vostok station temperature profile[7]

Conductivity calculation (pure ice) The calculate the conductivity for pure ice the parameterization reported by Matsuoka et al[6] is used. The imaginary part of the permittivity is given by the following formula The parameters A, B and C for different temperatures are given in table 1.The conductivity for pure ice can be calculated by the formula Table 1 [6]Matsuoka et al

Conductivity calculation (impure ice) There are two major type of impurities existing is antarctic ice which are acid ion H + and sea salt ion ssCl -. The formula used by Macgregor is only useful for the low frequency (<800MHz). To calculate the conductivity properly for the ANITA frequency band it has to be modified. It will take the following form Where can is calculated as before and the other impurity terms are given by the following formulae

Conductivity calculation (impure ice) The temperature dependence of the parameters and is given by Matsuoka et al shown in the following Figure shown on the right. The values of other parameters used in this study are as follows. These values are reported by Fujita et al[5], Matsuoka et al[6] and Hugh et al[8]. As the sea salt concentration varies more than the acid ion impurity concentration so three different values are 2, 4 and 20 micro moles per litre are used depending on the distance from the sea. These values are approximate. The work of collection of more precise concentration values for antarctica is under progress. [6]Matsouka et al

Conductivity calculation (pure and impure ice) Using the formulas and values mentioned in the previous slide, the pure and impure conductivity terms are plotted in the following plot. References for above plots [5] [6]

Attenuation Length calculation For attenuation length calculation, firstly the attenuation rate is calculated in dB/m by the formula. The real part of permittivity is given by as reported by Matsuoka et al The attenuation length in meters is given by

Modeled Attenuation Profiles(High depth areas)

Attenuation Profiles(low depth places)

Modeled Attenuation Profiles(Low depth areas)

South Pole attenuation model comparison

[9]Barwick et al

Ross Ice Shelf attenuation model comparison

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.

References (1) Amy Connolly, David Saltzberg “Summary of a Simulation of the ANITA Detector” August 13, (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: (2000) (6) Matsouka et al J. Phys. Chem B 101(1997) (7) I. A Zotikov “The thermophysics of glaciers”. (1986) (8) Hugh et al Geo. Phys Lett Vol. 20 No. 11(1993) (9) Barwick et al J. Glaciology Vol. 51, No. 173 (2005)