Coherent Wave Effects in Layering & Incoherent Model Inter-Comparison

1. Coherent Wave Effects in Layering&Incoherent Model Inter-Comparison UWBRAD meeting May 20, 2014 Leung Tsang, Shurun Tan, Tianlin Wang

2. Part I Physics behind coherent wave effects Magnitude of and depends on permittivity contrast – density fluctuation effects Phase difference depends on layer thickness – layer thickness variation effects

3. Model of Layering Effects Density profile: (Drinkwater 2004) Modified by damping Gaussian Noise (Macelloni and Brogioni) Standard deviation Damping factor Layer thickness: Layer thickness of the -th layer Average of layer thickness Standard deviation of layer thickness Total layer thickness

4. Reflection and Emission Effective permittivity: Maxwell-Garnett mixing formula Ice permittivity empirical model of Matzlerand Wegmuller, 2006 Absorption coefficient: No scattering effects included in current model. Focus on coherent wave interference.

5. Temperature Profile • Temperature profile (Jezeket al. 2013)

6. - frequency dependence • Tb of coherent model shows resonance for fixed layer thickness with density fluctuation. 150 realization

7. - frequency dependence • Incoherent model is not sensitive to layer thickness variation. • Tb of coherent model shows resonance for low frequency, and the resonance mitigates for higher frequency. • With moderate layer thickness variation, Tb of coherent model gets a minimum around 1GHz. 1950 realization

8. - frequency dependence • As the layer thickness increases, the number of layers decreases, of incoherent model increases because of fewer reflections. • As average layer thickness increases, coherent model experiences more resonance cycles. 150 realization

9. - frequency dependence • When average layer thickness is large, Tb of coherent model converges to incoherent model as standard deviation of layer thickness increases. 150 realization

10. - angular dependenceat 1.4 GHz 150 realization 150 realization Note there is no strong resonance over angle after statistical average. The difference in Tb between coherent and incoherent model is due to the resonance with respect to frequency.

11. Part II Incoherent model Inter-comparison Incoherent approach • Apply QCA-CP collective scattering model (with non-sticky spheres, low frequency solution) to calculate effective permittivity () and scattering coefficient. • Apply a multiple layer model • Apply the same temperature, density, layer thickness profile provided by Marco • Compare angular dependence of Tb at 1.4GHz Temperature profile with seasonal swing near surface

12. Smooth density profile Layer thickness: 0 to 100m 1000 layers 10 cm each 100 to 300m400 layers 50 cm each 300 to 3200m579 layers 5.0086m each At 3200m water base at ~269K (temp of the last ice layer) with ε=85.9 + 12.72i Grain radius: • Marco applies DMRT-ML • UW model without scattering agrees with Marco’s results because with Rayleigh scattering, mean cosine is 0. • UW model with scattering is about 4K lower because the non-physical approximation of the model

13. Noisy density profile 1 realization • Scattering is not included in the UW model • UW results agree with Marco’s results (slightly larger) when QCA-CP model is used to calculate effective permittivity and • UW Tb is lower by about 9K with Maxwell Garnett mixing formula to calculate effective permittivity and .

14. Noisy density profile 150 realization average • UW model with scattering is lower than UW model without scattering by about 3K. • UW model without scattering is slightly larger than Marco’s result for H-pol implying that the scattering effects accounts more with multiple reflection. • UW model with scattering is closer to Marco’s results also implying the increase of scattering importance with multiple reflection.