Penetration depth of Synthetic Aperture Radar signals in ice and snow: an analytical approach

Transcription

1 Penetration depth of Synthetic Aperture Radar signals in ice and snow: an analytical approach Michel Gay1, Laurent Ferro-Famil2 1 Grenoble Images Speech Signal and Control laboratory d Electronique et des Télécommunications de Rennes 2 Institut Workshop Remote Sensing and Modeling of Surface Properties. March 16, 2016

2 Penetration depth δp δp, defines the depth within a medium at which the power of a propagating wave is equal to e 1 of its power at the medium s surface (Ulaby et al. 1984). δp is a function of scattering and absorption losses within a medium, and can be calculated (Ulaby et al. 1984, Drinkwater 1989 ) by: δp = λ 1 q 4π {[1 + ( ε00 )2 ] 12 1} ε0 (1) ε0 2 λ : wavelength in free space ε0 and ε00 : real part and imaginary part of the dielectric permittivity δp represents the maximum depth within a medium that can contribute to the backscattering coefficient. 2

3 Snowpack: complex stratified dense medium δp assumes an incident field perpendicular to the snow surface From satellite, the incidence angle θi is different from Nadir. Using Snell s law and ε00 <<ε0 : θi θr δp0 δp cosθr 3 (2)

4 Contents 1 Ice 2 Snow 3 Electromagnetic backscattering model 4 Assimilation algorithm 5 Comparison between simulation EBM and experimental data 6 Conclude 4

5 Ice Permittivity of ice εi Ice, unlike water, is a medium substantially transparent to microwave with a permittivity εi : εi = ε0i + i ε00 i (3) In the field of microwaves, ε0i is frequency independent and only slightly dependent of the temperature T. This dependence may be modeled by the formula given by Mätzler et al.1987 ε0i = (T 273 K); 243 T 273 K (4) The proposed model by Hufford 1991 for ε00 i is a good compromise between the theory of Liebes s 1989 and the sets of data: α εi 00 = +β f (5) f α = ( θ). exp( 22.1 θ) θ 1+θ β = ( θ )2 1+θ with: θ = T0 /T 1 and T0 = 300 K and f, the frequency 5

6 Ice Permittivity of ice: ε00i Susceptibility in pure ice -1 The imaginary part of permittivity ε00 decreases with the temperature. -2 ε (ω) Hufford Model 273 K HM 268 K HM 258 K HM 243 K Matzler Model 258 K The permittivities have minimums between 0.9 GHz and 2.9 GHz -3 The Matzler model is slightly different Frequency (GHz) 6

7 Ice Penetration depth: δp0 Penetration depth in pure ice 3 Drinkwater 273 K 268 K 263 K θ i = 0 δcosθ i in meters 2 L-Band 1 C-Band 0 X-Band Ku-Band Ka-Band Frequency (GHz)

8 Ice Penetration depths: δp0 Microwave penetration depth δp0 (θi = 0 ) in solid ice at three temperatures. 263 K 268 K 273 K 1.55 GHz (m) GHz (m) GHz (m) GHz (m) GHz (m) The penetration depth decreases with increasing frequency. The temperature dependence of ice permittivity causes the penetration depth to decrease with temperature. At 30 GHz, this penetration depth is less than 2 m for K. 8

9 Ice δcosθ i in meters Penetration depth: δp0, with salinity S = 35 ppm 3 2 Penetration depth in ice Pure Ice 273 K Impure Ice 273 K Pure Ice 268 K Impure Ice 268 K 1 L-Band 0 C-Band -1 X-Band Ku-Band Ka-Band Frequency (GHz)

10 Snow Permittivity of snow: εef f We can perform the same type of calculation for snow The complexe effective permittivity of snow εef f is given by: 2 εef f = εg + j. δεg.k02 kg εb.ls3 3 with εg the quasi-static dielectric constant and δεg the variance of fluctuation (6)

11 Snow Penetration depth δp0 in dry snow, density dependence The density determines the absorption losses (Polder, Van Santen 1946 ). Below around 18 GHz, the penetration depth is smallest for solid ice. Above around 30 GHz solid ice has the largest penetration depth -> scattering losses dominate absorption losses. Between 18 GHz and 30 GHz for this temperature and crystal size, absorption losses and scattering losses are nearly equal. 11

12 Snow Penetration depth δp0 in dry snow, crystal size dependence Penetration depth in dry snow 3 Temperature = 268 K Solid Pure Ice -3 Snow : 400 kg m 0.2 mm Snow : 400 kg m mm Snow : 400 kg m-3 1 mm δ p in meters 2 1 L-Band 0 C-Band -1 X-Band Ku-Band Ka-Band Frequency (GHz) Snow crystal size affects scattering losses. Scattering increases with the ratio of the crystal size to the microwave length. Example: scattering losses for the same snow type are larger at Ku-Band than X-band -> the penetration depth decreases. Larger crystal sizes have smaller penetration depths. 12

13 Snow Penetration depth δp0 in dry snow, temperature dependence δp0 depends on snow type. For each snow type, in very high frequency, the dependence on temperature is not significant. Snow temperature changes are more significant below Ka-Band. Ex.: at X-band, snow type 2 has δp m for 253 K and δp m for 268 K. The change being due to absorption losses. 13

14 Snow Density affects absorption losses up to 20 GHz. Beyond this frequency, both absorption and scattering losses are involved. Crystal size mainly affect scattering losses. Temperature changes absorption losses. We use the determined permittivities in a backscattering model of electromagnetic waves of snowpack. 14

15 Electromagnetic backscattering model Multilayer electromagnetic backscattering model (L. Ferro-Famil, S. Allain, N. Longépé...) Three physical phenomena are taken into account to calculate σv0 : 1 0 Calculation of σsim : sum of three coefficients σsim = σas + σv + σg0 Attenuation : SFT -> εef f -> Ke 2 Scattering : SFT-> phase matrix 3 Refraction : transmission matrix T σv0 : (7) DMRT (Longépé et al., 2009) 0 and σ 0 : IEM (Fung et al., 20). σas g 15

16 Electromagnetic backscattering model 16

17 Assimilation algorithm Assimilation algorithm SAR data (X.V. Phan). 17

18 Comparison between simulation EBM and experimental data Sodankyla: ground Radar, stratigraphic profiles, TerraSAR-X acquisition Ground Radar observation-> SnowScat instrument Parameters Frequency GHz Incidence 30o <θ<60o Polarisation HH, HV, VH, VV Stratigraphic snow profiles 18

19 Comparison between simulation EBM and experimental data With our assimilation algorithm we can modify the observed stratigraphic profiles of snow (incidence angle θi = 30 ). Backscatter coefficients calculated σsim =σas +σvol +σsg converge well to the values measured by the ground radar at Ku band (16.7 GHz) and X band (.2 GHz) 19

20 Comparison between simulation EBM and experimental data New stratigraphic snow profiles are used to simulate the backscattering σsim at incidence angle θi = 40 and θi = 50. We have a good agreement between the backscatter coefficients calculated and measured at X-Band and Ku-Band. At these two frequencies in VV polarization, the most significant contributions to the variation in backscattering are grain size and roughness of snow ground interface. 20

21 Comparison between simulation EBM and experimental data In the same way, we can assimilate the backscattering σassim in polarization HH at incidence angle θi = 30 and simulate the backscattering σ0 at θi = 40. Again, we have a relative good agreement between the backscatter coefficients calculated and measured at X-Band and Ku-Band. 21

22 Conclude Future works Continue the identification of EBModel Study the range of validity of the model in VV and HH polarization. Characterize effects of: incidence angle, roughness parameters, grain size, layer thickness, volumetric liquid water content... Compare with other models. Use this model to assimilate radar satellite data: TSX, CSK, and Sentinel. 22

23 Conclude Thank you for your attention Publications M. Gay, X.V. Phan, L. Ferro-Famil, F. Karbou, Y. Durand, G. D Urso, and A. Girard. Simulation de la rétrodiffusion radar du manteau neigeux, comparaison avec les données d un radar sol et TSX (projet NoSRex) ENVIREM, Paris X.V. Phan, L. Ferro-Famil, M. Gay, Y. Durand, S. Morin, S. Allain, G. D Urso, and A. Girard, 1D-Var multilayer assimilation of X-band SAR data into a detailed snowpack model. Cryopsphere, 8, p , X.V. Phan, L. Ferro-Famil, M. Gay, Y. Durand, M. Dumont. Comparaison between DMRT simulations for multilayer snowpack and data from NOSREX project. IGARSS L. Ferro-Famil, C. Leconte, F. Boutet, X. V. Phan, M. Gay, and Y. Durand. PoSAR: a VHR tomographic GB-SAR system Application to snow cover 3-D imaging at X and Ku Bands, in 9th European Radar Conference (EuRAD 2012), (Amsterdam, Pays-Bas), Oct