1. Radiation Laboratory Snowpack Microstructure Characterization and Scattering Models Using DMRT and A Fully Coherent Approach Leung Tsang 1 and Kung-Hau Ding 2 1 Department of EECS, Radiation Laboratory, University of Michigan, Ann Arbor, MI, USA 2 Air Force Research Laboratory, Wright-Patterson AFB, Dayton, OH, USA Monday, July 13, 2015 2:30-3:00 PM

2. Radiation Laboratory Outlines  Dense Media Radiative Transfer (DMRT) : Partial Coherent Approach  Snow Microstructure Characterization  Validation: Active and Passive Measurements  Fully Coherent Approach : Solve Maxwell Equations for a Layer of Snow Over Ground  Bistatic scattering: 2D and 3D simulations  Tomography, FACF: 2D simulations  Open Source Code : DMRT-QMS-A&P 2

3. Radiation Laboratory Dense Media Radiative Transfer Equation: 3

4. Radiation Laboratory DMRT (1) Phase Matrix for a Collection of Ice Grains Calculated by Solving Maxwell Equations Including coherent interactions a) QCA for spheres b) Foldy-Lax for spheres c) DDA for bicontinuous medium (2) Substitute Phase matrix into Radiative Transfer Equation and then solve Radiative Transfer Equation (3) DMRT is a Partial Coherent Approach 4 Dense spheres Bicontinuous media

5. Radiation Laboratory Bicontinuous Media: Computer Generation 5 Depth Hoar (30%) 3 cm * 3 cm picture Depth Hoar (30%) 3 cm * 3 cm picture Computer generated snow A. Wiesmann, C. Mätzler, and T. Weise, "Radiometric and structural measurements of snow samples," Radio Sci., vol. 33, pp. 273-289, 1998. real snow

6. Radiation Laboratory Discrete Dipole Approximation (DDA) with FFT 6 Discretized volume integral equation Each cube has a dipole moment Sample Number KcKc zpzp Fraction Volume 315001020% 1310001030% 1615001040% 1810005020% extinction coefficients agree with experimental data Experiment, Radio Laboratory, Helsinki University of Technology in 1987 DDA includes coherent interactions among inhomogeneity

7. Radiation Laboratory Phase Matrix of Bicontinuous media 7 Size parameter b o Scattering coefficient decreases as size parameters b increases o Mean cosine decreases as size parameters b increases Phase matrix depends on the level of ice grain aggregations.

8. Radiation Laboratory Snow Microstructure Characterization Quantitative Comparison A. Wiesmann, C. Mätzler, and T. Weise, "Radiometric and structural measurements of snow samples," Radio Sci., vol. 33, pp. 273-289, 1998. Computer- generated bicontinuous medium Real snow cross section image Simulated Sticky Spheres Sticky Sphere and Bicontinuous Medium 8

9. Radiation Laboratory Correlation Function Snow Microstructure - Indicator function: For each point in space, assign 0 to air and 1 to ice - compute correlation function Performed by Prof Kong’s Group and M ӓ tzler’s Group real snow snow of bicontinuous media snow of spheres and sticky spheres For real snow  Found Close to exponential correlation function for short distance  Exponential decreases to zero quickly at large distance 9

10. Radiation Laboratory Correlation Function of Bicontinuous Medium 10 exponential correlation function for short distance Tails of correlation functions represent large grains and clusters

11. Radiation Laboratory Correlation function for spheres 11

12. Radiation Laboratory Recently, from Pair Distribution Functions, Derive Correlation Function: Sticky particles has correlation function that has longer tail 12 Fraction volume = 30%; diameter = 2.0 mm. Pair distribution function of sticky spheres Correlation function of sticky spheres

13. Radiation Laboratory Correlation function: grain size distributions 13 Pair distribution function of multiple-size spheres Correlation function of size distributions

14. Radiation Laboratory Normalized covariance functions of QCA multiple- size, QCA-sticky and bicontinuous model Correlation functions are close to exponential for short correlation distances Exponential correlation functions neglect the tails Tails in correlation functions at larger distance indicate large grain aggregation. Larger clusters of grains give non-Rayleigh scattering. Correlation Functions: a common point of comparison between real snow and computer snow 14

15. Radiation Laboratory Validation of Bicontinuous DMRT: Active and Passive Measurements Total 12 channels Same physical parameters for active and passive and multiple frequency channels ◦ Radiometer: V and H at 10.65, 18.7, and 36.5GHz  6 Channels ◦ Scatterometer: VV and VH at 10.2, 13.3, and 16.7GHz  6 Channels 15

16. Radiation Laboratory Active and Passive Campaign for ESA CoReH2O at Sodankyl ӓ, Finland ◦ Four successive winter seasons: Nov. 2009 ~ May 2013 ◦ Tower based time series measurements at Sodankyl ӓ, Finland ◦ Ground measurements: SWE, bulk density, snow depth, snow grain size, snow stratification, snow temperature, air temperature, soil temperature, soil moisture etc. 16

17. Radiation Laboratory NoSREx Measurement Setup SnowScat Scatterometer and SodRad and Elbara-II radiometer Multiple incidence angles of 30, 40, 50 and 60 incidence angles SnowScat Azimuthal angles spanning 96 degree SnowScat mounted at the height of 9.1m, SodRad at 4.5m Snowpit measurement conducted with both SnowScat and SodRad measuring the same spot 17

18. Radiation Laboratory Ground Measurements 18

19. Radiation Laboratory backscatter against SWE for vertical co-pol at 10.2GHz, 13.3GHz, and 16.7GHz backscatter against SWE for cross-pol at 10.2GHz, 13.3GHz, and 16.7GHz brightness temperature against SWE at (a) 10.65GHz, (b) 18.7GHz and (c) 36.5GHz Good comparison for Co-Pol between Model and Experiments Good correlation with SWE for 13.3GHz and 16.7Ghz 10.65GHz, 18.7GHz and 36.5GHz Tb show good correlation with SWE Good agreement between model and measurements for both pols. Model Comparisons with Active/ Passive Measurements 19

20. SOLVE MAXWELL EQUATION FOR ENTIRE PROBLEM: SNOW OVER GROUND from partial coherent to fully coherent 20 Do not use DMRT! Why: SAR is coherent; measured scattered wave has amplitude and phase; DMRT has intensity which is amplitude squared Solving Maxwell Equations entirely give Amplitude and Phase

21. Radiation Laboratory 21 Fully Coherent Approach: Solve Maxwell Equation of a Layer of Snow Over Ground Half Space Green’s Function With half space Green’s function: Two Terms DDA with Half Space Green’s function Usual DDA only has 1 term in Green’s function

22. Radiation Laboratory 2D Simulations 22 o 2D means cylindrical structure invariant perpendicular to the incidence plane o Though not real life, but can give important physical results

23. Radiation Laboratory 23 Incidence angle: 40 degree Number of realization: 1000 40 degrees specular scattering -40 degrees backscattering Backscattering enhancement with angular spread 10~15 degree Bistatic Scattering : Intensity Incident direction and plot of scattering in all directions

24. Radiation Laboratory 3D Real Life Problems: High Performance Parallel Computing 24 dimension# of cellsmemory# of coreswall time 160GB5043.5 min 320GB10029.1 min 640GB20068.5 min Recorded computing resources usage on U Michigan FLUX cluster -Each processor (core) owns 4GB memory, -Each nodes supports up to 16 processors/ cores (standard configuration) -Memory of the same node is shared among processors. Time is for one realization, viz. solving DDA equation twice for two different incidence polarizations.

25. Radiation Laboratory 3D Bistatic Scattering Simulation: Comparison with DMRT Notable peak near backscattering direction Overall trend of incoherent bistatic scattering coefficients agree with DMRT 25

26. Radiation Laboratory GBSAR Tomography Measurements: Measure Amplitude and Phase : to Image layering Structures Multi-baseline Tomo-SAR can potentially show snowpack layer structures. GBSAR (ground based SAR): X (8.2 ~ 12.2GHz); Ku (12.2 ~ 16.2GHz) Aperture in elevation: 30~50 degrees Aperture in azimuth: ~30 degrees, ~3m Ground range coverage: 6~8m Tomographic processing: time domain back projection algorithm Ref: S. Tebaldini and L. Ferro-Famil, “Retrieved vertical structure consistent with snowpack hand-hardness from snow-pit measurement,” ESA AlpSAR Final Report, 2014 The normalized backscattering intensity tomogram (dB) obtained at Ku band with corresponding snow pit measurement Ref: L. Ferro-Famil, S. Tebaldini, M. Davy, and F. Boute, “3D SAR imaging of the snowpack at X- and Ku-Band: results from the AlpSAR campaign,” EUSAR 2014 26 Top layer Bottom layer Top layer Bottom layer Ground

27. Radiation Laboratory Limitations on Airborne / Space borne SAR Tomography 27 different from medical tomographic imaging  Backscattering only  Small frequency range  Small angular range Tomography with field imaging

28. Radiation Laboratory 2D Simulation: two layers of snow over ground 28 Snow structure: Reconstructed tomogram (field imaging), TE  frequency range ◦ 9~11 GHz, Step: 100MHz  Incidence angle range ◦ 30~50 degree, Step: 1 degree Radar observation:

29. Radiation Laboratory Frequency and Angular Correlations: FACF imaging Field imaging: image both vertical and horizontal FACF imaging o Use frequency and angular correlations o To suppress scattering from ice grains so as to reveal the layered structure 29

30. Radiation Laboratory Comparison of two imaging approaches 30 Field imaging o 2D Fourier transform of Multi-frequency and Multi-angle measurements Correlation imaging (FACF) ◦ suppress scattering from ice grains which has little correlations ◦ layering interfaces and grounds has stronger correlations

31. Radiation Laboratory Summary of Microwave Scattering in Snowpack Correlation function: snow microstructure, compare real snow and computer snow ◦ Exponential correlation function is for short range ◦ Tails in correlation function of sticky spheres, size distributions, and bicontinuous media represent large grains Partial Coherent Model ◦ DMRT with Maxwell Equations Based Phase Matrices ◦ Model validated by active and passive measurements, 12 channels Fully Coherent Approach: SAR, InSAR, Tomo-SAR are coherent with amplitude and Phase ◦ Fully Coherent Approach: Numerical solutions of Maxwell Equations for the entire problem; without DMRT ◦ Tomo-SAR: to retrieve snow stratigraphy from coherent microwave imaging 31

32. Radiation Laboratory Open Source DMRT-QMS-A&P Model Open Source (since 09/2014) ◦ http://www.ee.washington.edu/research/laceo/DM RT-QMS.html http://www.ee.washington.edu/research/laceo/DM RT-QMS.html Characteristics ◦ Active and passive remote sensing of snow ◦ Multiple-layered snowpack ◦ Includes multiple scattering effects ◦ Scattering model of QCA with sticky spheres ◦ Built-in NMM3D rough surface lookup table for backscattering ◦ Fully polarized ◦ Code written in Mat lab ® 32

33. Radiation Laboratory DMRT-QMS-A&P Interfaces: Inputs 33 Step 1. Prepare a snowpack description file: * to run the active model Step 2. Modify and run script test_DMRT_QMS_active.m -Specify incidence angle -Specify frequency -Specify snowpack description file -Specify ground permittivity -Support Mironov soil permittivity model -Specify the ground roughness -Choose a surface scattering model -Support NMM3D LUT -Support 1 st order SPM3D -Support Oh model * to run the passive model Step 2. Modify and run script test_DMRT_QMS_passive.m -Specify frequency -Specify observation angle (optional) -Specify snowpack description file -Specify ground permittivity -Support Mironov soil permittivity model -Specify the ground roughness -Support QH model -Support Wegmuller and M ӓ tzler 1999 model

34. Radiation Laboratory DMRT-QMS-A&P Interfaces: Outputs Active: ◦ Print out backscattering coefficients Passive: ◦ Plot out the brightness temperature pattern ◦ Print out the brightness temperatures at the specified observation angle. 34 vv = -8.9751; (vol: -10.4506, surf: -14.3804) hh = -8.3403; (vol: -9.3555, surf: -15.1502) hv = -19.9032; (vol: -21.9407, surf: -24.1691) vh = -19.9034; (vol: -21.9409, surf: -24.1691) TB at 55.0 degree: v 257.77(K); h 236.98(K) Example outputs of the default test scripts: Two layer snowpack as specified in the demonstration file. Active: 17.2GHz, 40 degree Passive: 18.7GHz

35. Radiation Laboratory 35