1 A Broad-band Radio Attenuation Model for Antarctica and its effect on ANITA sensitivity By Amir Javaid University of Delaware

2 Topics ● Radio Attenuation in ice and ANITA sensitivity ● Dependence of Radio Attenuation in ice on electrical conductivity and other physical and chemical properties of Antarctic ice ● Electrical conductivity calculation ● Attenuation estimation techniques ● Attenuation model Results ● Effects of new attenuation model on effective volume estimation

Attenuation in ice and ANITA sensitivity UHE neutrinos produce Radio pulses when they interact in Antarctic ice One of ANITA’s goal is to catch these Radio pulses in order to detect UHE neutrinos UHE neutrino interactions can be very deep inside Antarctic ice Radio pulses attenuate as they propagate inside ice Proper understanding of radio attenuation in ice is essential for better detection

Dependence of Radio Attenuation in ice on physical and chemical properties of Antarctic ice

Carriers of conduction in polar ice Impure ice (MacGregor[2]) Pure Ice (Physics of ice)

6 Conductivity calculation method (pure ice) Table 1 [1]

7 Conductivity calculation method (impure ice)

Conductivity vs frequency

Conductivity vs Temperature

10 Impurity data location maps(ITASE) (Bertler et al.)[4]

11 Impurity data location maps(ITASE) All impurity locations

12 Method for conversion from major ions to [H + ](acid) and [ssCl - ](Sea Salt) ● [H + ] concentration The [H + ] concentration can be estimated by the following charge balance equation [H + ] = [Cl - ] + [NO - 3 ] + 2 [ssSO 4 2- ] + [xsSO 4 2- ] +[CH 3 SO - 3 ] - 2 [Ca 2+ ] - [K + ]-2 [Mg 2+ ] -[Na + ], ● [ssCl - ] concentration The sea salt Chlorine concentration can be calculated by using the of ratios F X of different ionic concentrations with sea salt Sodium ion in sea water. This can be represented as following F X =[ssX]/[ssNa + ] The [ssNa + ] concentration in the sample is calculated by [ssNa + ] sample =min([X] sample /F X ) Where [X] sample is the value of ionic concentration of some ion X in the sample. The sea salt concentrations of other ions in the sample can be estimated by the formula F X =[ssX] sample / [ssNa + ] sample The non sea salt ionic concentration [xsX] sample can be calculation by [ssX] sample =[ssX] sample +[xsX] sample

Impurity concentration data  The ITASE data consists of major ions including sodium (Na), magnesium (Mg), calcium (Ca), potassium (K), chloride (Cl), nitrate (NO 3 ), sulphate (SO 4 ), and methane sulfonate (MS). Bertler et al.[4].  The data includes total of 520 points around Antarctica. For this study 326 points are used because of missing values of some major ion concentrations. To estimate some of the missing data, data fitting has been performed. The plots on the right show the fitting. 13

14 IDW method for impurity concentration interpolation

kriging Kriging is a group of geo-statistical techniques used for estimation of value and variance of the value of a random field at location where there is no data available by using locations with available data. It is a method based on linear prediction also known as Gauss-Markov estimation or Gaussian regression process. Major types of Kriging include Simple Kriging, ordinary kriging, cokriging and some more specialized types. We have used ordinary kriging for the present work. Application areas of kriging o Environmental science o Black box modeling in computer experiments o Hydrogeology o Mining o Natural resources o Remote sensing

Kriging interpolation method

17 Comparison of Acid impurity IDW and Kriging

Comparison of IDW and kriging(contd..) To compare the two models of impurity estimation we have performed an n-1 check. This check involves taking one value out of the data and estimation of that value by using the rest of the data. The results for both IDW and kriging are shown below. It is very clear from these plots that the estimation from kriging is more accurate and it also provides an estimation of error also which is not possible by IDW.

3D Temperature Model for Antarctica 19 A 3D temperature model has been used for the present study. Data for this model is provided by Dr. James Fastook, University of Maine, extracted from UMISM, the University of Maine Ice Sheet Model, a multi-component model of ice-sheet physics. A detail account of the model, reference and publications can be found at the following website The interpolation scheme utilized to interpolate between the grid points uses two kinds of weights which are the following ● Inverse square radial distance weights ● Inverse square ice thickness difference weights The maximum radial distance used is 200 km and only those profiles are used which has a depth difference of less than 200m from the required location depth.

Temperature Profile Sample 20

Comparison of Modeled Temperature profiles with Measured profiles

22 Attenuation model Results with IDW (Full Path attenuation)

23 Attenuation model Results with IDW (1km(max) one way Path attenuation)

24 Attenuation Results with kriging(Full path)

25 Attenuation Results with kriging(1km max depth one way)

Attenuation Results with kriging(Attenuation depth profile)

Kriging vs IDW(0.6GHz) Full depth bed return power loss Top 1km (max) power loss

28 Comparison with South Pole and Ross Ice Shelf measurements (Barwick et al [5]) David Saltsburg

Implementation of Kriging attenuation model in icemc  A grid was prepared with (latitude, longitude, depth, frequency).  The grid comprises of 5329 latitude longitude bins, 100 depth bins and 15 frequency bins.  The code calculates attenuation values for only 8 set of frequencies inside the ANITA bandwidth integrated over a vertical direct and reflected ray paths, starting from the point of the origin to the surface.  The values of attenuation for the rest of the frequencies are calculated by linear interpolation.  The estimation of the attenuation grid points are done by the weighted estimation method similar to the one used for temperature estimation.

Comparison of Effective volume*steradians (Kriging vs icemc attenuation)

Icemc Run results(both rays) (2million events) Energy(eV) (kriging attenuation) # of Unweight neutrinos passing trigger Direct # of Unweight neutrinos passing trigger Reflect Energy(eV) (Icemc attenuation) # of Unweight neutrinos passing trigger Direct # of Unweight neutrinos passing trigger Reflect

Un-weighted Events passing trigger

Comparison of Effective volume*steradians (Kriging vs icemc attenuation)(Reflected Rays only)

35 Plan ● Submit the attenuation model paper to Journal of Geophysical research for publication.

36 References 1. Fujita et al. Physics of Ice Core Records: (2000). 2. Joseph A. MacGregor et. al J. Geophys. Res 112 (2007). 3. Matsuoka et al. J. Phys. Chem. B, 101, (1997). 4. Bertler et al. Ann. Glaciol. 41, (2004). 5. Barwick et al. J. Glaciol. 51(2007). 6. Numerical Recipes 3 rd Edition, Cambridge University Press(2007). 7. Sacks, J. and Welch, W.~J. and Mitchell, T.~J. and Wynn, H.~P. (1989). Design and Analysis of Computer Experiments. 4. Statistical Science. pp. 409– Hanefi Bayraktar and F. Sezer. Turalioglu (2005) A Kriging-based approach for locating a sampling site—in the assessment of air quality, SERRA, v.19, n.4, DOI /s , p Chiles, J.-P. and P. Delfiner (1999) Geostatistics, Modeling Spatial uncertainty, Wiley Series in Probability and statistics. 10. Zimmerman, D.A. et al. (1998) A comparison of seven geostatistically based inverse approaches to estimate transmissivies for modeling advective transport by groundwater flow, Water Resource. Res., v.34, n.6, p Tonkin M.J. Larson (2002) Kriging Water Levels with a Regional-Linear and Point Logarithmic Drift, Ground Water, v. 33, no 1., p , 12. Journel, A.G. and C.J. Huijbregts (1978) Mining Geostatistics, Academic Press London 13. Andrew Richmond (2003) Financially Efficient Ore Selection Incorporating Grade Uncertainty), Mathematical Geology, v. 35, n.2, p Goovaerts (1997) Geostatistics for natural resource evaluation, 15. X. Emery (2005) Simple and Ordinary Kriging Multi-gaussian Kriging for Estimating recovevearble Reserves, Mathematical Geology, v. 37, n. 3, p ) 16. A. Stein, F. van der Meer, B. Gorte (Eds.) (2002) Spatial Statistics for remote sensing