Joel T. Johnson, K. C. Jezek , L. Tsang, C. C. Chen, M. Durand, G. Macelloni Biweekly Telecon

1. UWBRAD: Ultra-Wideband Software-Defined Microwave Radiometer for Ice Sheet Subsurface Temperature Sensing Joel T. Johnson, K. C. Jezek, L. Tsang, C. C. Chen, M. Durand, G. Macelloni Biweekly Telecon 22nd April 2014 Columbus, OH

2. Project Status • First increment of funds in place at OSU as of 4/10; start date 4/1 • ~ 57% of year 1 budget • OSU separate account for BPRC project • OSU contracts working on getting UW subcontract in place • OSU team working on getting purchase order to Leuski • Andrews/Leuski/Johnson reviewing radiometer front end design • Some components no longer available • Also investigating calibration procedures • Also reviewing digital backend component selection • Pentek, Inc. or Agilent also provide high speed sampling boards • Need to make selection soon • AlazarTech board apparently can be purchased with wider analog bandwidth option • Still no cost quote from Ken Borek Airlines

3. Kickoff Meeting Wrapup • April 10th; NASA IIP program manager ParminderGhuman attended • Tom Wagner (NASA Cryosphere manager) also invited but did not dial in • No major concerns expressed; bimonthly reports will be required • Try to stay up-to-date on spending! • This project may be more suited for eventual long term airborne deployment (high altitude) instead of space • Will need to complete a TRL level spreadsheet at some point showing activities that will advance TRL level if achieved successfully

4. Model Comparisons • A code intercomparison makes sense as a first activity in the modeling/retrieval arena • Goal: have a first set of comparisons by mid-May • Models to compare: • DMRT-ML (Aksoy/Macelloni/Brogioni) • Coherent wave approach (Tsang) • Bicontinuous medium approach (Tsang)? • MEMLS (Durand) • 0th order RT (Jezek) • Simulating the DOME-C environment to start with makes sense since tower measurements are available

5. Model Requirements • Output Tb as a function of: • frequency from 0.1-3 GHz, 0.1 GHz steps • 0 to 60 degrees incidence angle • H- and V- pols • Marco has produced reasonable match to DOME-C data already using DMRT-ML using “layered method” (i.e. Monte Carlo average of many random layers) • Proposal: Use Marco’s “best” fit parameters; compare: • i) results with no “layering” • Ii) results for one realization with “layering” (need to specify file) • Iii) results after averaging over 100 realizations with “layering” • Iv) consider “rock” or “ice” or “water” at base of icesheet

6. Model analysis: inputs The model used in this work was the DMRT-ML which was developed under the Quasi-Crystalline Approximation with Coherent Potential - QCACP (implemented at LGGE). It simulates the snowpack emission under the Rayleigh approximation. The input to the model were: -Snowpack temperature profile 0 -10 m : seasonal temperature swing (Bingham and Drinkwater, 2000). 0 to 10m Tm = mean annual value ; Ta = seasonal T amplitude. below 10 m : (Jezek et al. 2013) • The match of the two formula is performed at 10m below the surface

7. Model analysis: inputs Tsurface (July) Tsurface (January) T meanannualvalue G = 53.3*10^-3 geothermal heat flux M = 50*10^-3 accumulation rate mel = 0.7*10^-3 basal melting rate H = 3200 altitude Kc = 2.7 thermal conductivity Kd= 45 thermal diffusivity Ts= 217 temperature at the surface

8. Model analysis: inputs -Snowpack density profile The density profile was obtained by slightly modify the one in Bingham and Drinkwater for coarse grains in order to fit the measurements collected at Dome C. -Snowpack grain radius profile The grain radius profile was the one published in Zwally adjusted to fit the Tb measurements at L- and C- band -Layers profile In order to better analyze the problem and to speed up the computations we considered: 0 to 100m  1000 layers 10 cm each 100 to 300m  400 layers 25 cm each 300 to 3200m  480 layers 6 m each Below 3200  pure ice – half medium In case of the C-band the number of layers has been limited to 1402 (approx. 301m) because of the lower penetration depth.

9. Model analysis: layering - Real data shows fluctuation of density and grain radius along the profile - Density and grain radius profiles where perturbed with a dumped gaussian noise where and are the standard deviation of the gaussian noise. Ground Measurements at Dome-C

10. Model analysis: obtainedresults For σ=60 Kg/m3 and α=30 m weobtain L-band C-band Tb (K) Tb (K) Angle (deg) Angle (deg) • The introduction of fluctuations in the snowpack density profile makes possible: • to fit quite well the experimental measurements • to reproduce the difference between V and H polarizations • to reproduce the trend of the V pol

11. Modeling of Polar Ice Sheet Emission 0.5 GHz to 2 GHz UWBRAD teleconference Leung Tsang, Shurun Tan, Tianlin Wang 04/08/2014

12. Outline • Review of the DMRT-ML model • Density Fluctuation Modeling using coherent wave approach • Snow/Ice modeling with bicontinuous Medium • Review of the Bicontinuous medium/DDA/DMRT approach and key results • Model ice sheet with bicontinuous medium

13. Current Model - DMRT-MLboth reflections and volume scattering • volume scattering • Snow: ice grains in air background • Ice: air bubbles in ice background • QCA-CP models • Spheres<<wavelength • Extinction takes into account packing effect and sticky effects • Rayleigh phase matrix and • reflections of layers • Incoherent additions of reflections The snowpack viewed by DMRT-ML G. Picard, et.al, Simulation of the microwave emission of multi-layered snowpacks using the dense media Radiative transfer theory: the DMRT-ML model, Geosci. Model Dev., 6, 1061-1078, 2013.

14. Wave approach of Density Fluctuation Effectsreflections only, no volume scattering • Measurement shows fine scale (5cm-10cm) density fluctuation • UWBRAD frequency range 0.5GHz~2.0GHz, with wavelength 15cm~60cm. Layer thickness is smaller than wavelength. • Coherent wave interaction between successive layers • Compare results of wave approach and DMRT approach Figures from Macelloni and Brogioni, UWBRAD Teleconference , 03/01/2013

15. Brightness temperature Modeling for layered ice sheet with internal temperature distribution • Fluctuation Dissipation Theory • Dyadic Green’s function for stratified medium A, B, C, D are the upward and downward going wave coefficients in each layer for TE and TM polarization, respectively

16. Antarctica Ice sheet Density Profile setup Density profile from Drinkwater, 2004; and from Macelloni and Brogioni, UWBRAD Teleconference , 03/01/2013 Standard deviation Damping factor Effective permittivity, spheres , Maxwell-Garnett mixing formula Ice permittivity, Mӓtzler and Wegmuller, 2006 Absorption coefficient estimated from effective permittivity

17. Antarctica Ice Sheet Temperature Profile Temperature profile Temperature profile following Aksoy and Johnson, UWBRAD teleconference, 02/25/2014

18. Brightness Temperature of ice sheet with density fluctuation One realization Monte Carlo analysis with 300 realization Non-uniform layer thickness , a total of 5100 layers

19. Snow/Ice sheet modeling with bicontinuous medium • Review of the Bicontinuous medium/DDA/DMRT approach • Model ice sheet with bicontinuous medium

20. EM Scattering Models: Bicontinuous • Computer-generated snow samples • Solve Maxwell equations numerically • To calculate effective permittivity, absorption/scattering/extinction coefficient and phase matrix • Combine with DMRT equations to predict brightness temperature and backscattering

21. Bicontinuous Medium Generation • Computer generated snow versus real snow picture Depth Hoar (30%): 3 cm * 3 cm A. Wiesmann, C. Mätzler, and T. Weise, "Radiometric and structural measurements of snow samples," Radio Sci., vol. 33, pp. 273-289, 1998.

22. Bicontinuous Parameters • Bicontinuous parameters: density, <ζ>, b • One to one relation between α and fV • Size parameter <ζ> • Mean wave number, relating to inverse of mean grain size • Size parameter b determines the size distribution • Related to clustering • Size distribution becomes uniform as b increases • ζnfollows Γ-distribution

23. Dependence on the Size Parameter <ζ> • The mean grain size changes

24. Dependence on the Size Parameter b • Clustering changes

25. Specific Surface Area (SSA) • Definition: surface area per unit mass [cm2/g] • Analytical expression • Numerical SSA • Use digitized pictures of snow; Discretize according to microwave resolution • Count ice surfaces contacting with air Example: <ζ>=6000 [m-1], b=1.5, fV=30% Bicontinuous SSA=71.8 [cm2/g] <ζ> = 5000 [m-1] fV= 0.2

26. Auto-Correlation Function • Analytical expression • Comparison with exponential correlation function in linear scale

27. Solve Maxwell’s Equations Numerically • For each computer-generated sample, Maxwell Equations are solved numerically based on DDA • Volume integral equation • DDA in each cube • Matrix equations • Matrix-vector product sped up by FFT

28. Model ice sheet with bicontinuous medium – Real Snow/Ice cross section images Representative vertical cross section micro-CT images of firn column from Summit, Greenland. Ice is white and the pores are black. Image size 8mm x 8mm. Lomonaco et. al, Journal of Glaciology, 57 (204), 755-762.

29. Model ice sheet with bicontinuous medium – Computer generated Snow/Ice cross section images Bicontinuous medium cross sectionsresampled into cubes. Ice is white and air pores are black. Image size 8mm x 8mm. Ice fractional volume varies from 0.2 to 0.9.

30. Quantifying the geometry SSA = 5.56m2/kg Correlation length = 0.241mm (exponential) SSA = 0.765m2/kg Correlation length = 0.197mm (exponential)

31. Characterizing EM property • Solve Maxwell’s Equation for each computer generated sample to calculate • Effective permittivity • Absorption/Scattering/Extinction coefficient • Phase matrix Discrete dipole approximation (DDA)