1. Introduction Model Results obtained Conclusions
An empirical approach towards
characterization of Dry Snow layers using
GNSS-R
Fran Fabra1 , E. Cardellach1 , O. Nogu´s-Correig1 , S. Oliveras1 ,
e
S. Rib´1 , A. Rius1 , G. Macelloni2 , S. Pettinato2 and S.
o
D’Addio3
1 ICE-CSIC/IEEC,Spain
2 IFAC/CNR,Italy
3 ESA-ESTEC, Netherlands
IEEE International Geoscience and Remote Sensing Symposium
July 24-29, 2011, Vancouver, Canada

2. Introduction Model Results obtained Conclusions
Outline
1 Introduction
2 Model
3 Results obtained
4 Conclusions

3. Introduction Model Results obtained Conclusions
Outline
1 Introduction
2 Model
3 Results obtained
4 Conclusions

4. Introduction Model Results obtained Conclusions
The frame of this work
GPS-SIDS project: Sea Ice - Dry Snow
GOAL: to investigate the use of reflected GPS signals to study sea ice
and dry snow properties from Space
METHOD: to collect long term data sets from fixed platforms (2 field
campaigns) and then extrapolate the results
CHALLENGE: experimental campaigns under polar environmental
conditions
Many institutions involved: ICE-CSIC/IEEC, GFZ and IFAC/CNR
(funded by ESA)

5. Introduction Model Results obtained Conclusions
Experimental campaign
Location
Dome Concordia (Antarctica)

6. Introduction Model Results obtained Conclusions
Experimental campaign
Location
Dome Concordia (Antarctica): American tower

7. Introduction Model Results obtained Conclusions
Experimental campaign

8. Introduction Model Results obtained Conclusions
Experimental campaign
Main aspects I
Instrument controlled in-situ by IFAC in coordination with IEEC.
Short campaign due to stability (DOMEX experiment [Macelloni et al., 2006])
of the dry snow cover: 10th to 21st December 2009
Antennas on top of American tower with a height of 46m.
Not a single surface: reflected signal as a contribution from different layers.

9. Introduction Model Results obtained Conclusions
Experimental campaign
Main aspects II
Maximum elevation achievable through a GPS reflection of 65◦ due to
limitations of the satellites constellation at these Latitudes.
Minimum elevation of 5◦ given by GOLD-RTR’s internal GPS receiver.
Monitorization area of ∼400m x 400m: pristine snow.
0˚
345˚ 15˚
32
˚ 30
330 ˚
0˚ 28
10
5˚
˚
31
24
20
˚
30
0˚
˚ 20
30
40
PRN
˚
16
50
˚
285˚
60
˚ 12
70
˚
8
270˚
4
255˚

10. Introduction Model Results obtained Conclusions
The instrument employed: GOLD-RTR
GNSSR dedicated hardware receiver
GPS L1 (1575.45 MHz)
C/A code (Public and with simple
autocorrelation)
10 channels compute cross-correlations
(waveforms) of 64 lags every millisecond
50 ns lagspacing ⇒∼ 15 meters
Scan the delay- and/or Doppler-space
3 radio front-ends
One Up-looking antenna for reference signal
(internal GPS receiver)
A dual polarization (LHCP and RHCP)
Down-looking antenna for reflected signals
Designed, manufactured, and tested at the
ICE-CSIC/IEEC

11. Introduction Model Results obtained Conclusions
Outline
1 Introduction
2 Model
3 Results obtained
4 Conclusions

12. Introduction Model Results obtained Conclusions
Motivation
Existing Model [Wiehl et al., 2003]: sub-surface contribution essentially given by
volumetric scattering.
But we consider volume scattering negligible compared to absorption loss.
Motivation: data shows clear interference fringes, better explained by
multiple-layer reflections.
20
Amplitude (a.u.)
15
10
⇒ Need to develop our own model
5
0
44.00 44.25 44.50 44.75 45.00
Elevation angle (deg)

13. Introduction Model Results obtained Conclusions
Multi-layer Single-reflection model: MLSR
Multiple infinite parallel layers
1 single reflection per layer is considered
Only LHCP reflections reach the receiver
Expressions
k=i k=i
Hk
ρi = ρ0 + 2nk −( Dk )sin(θ0 )
k=1
cos(θk ) k=1
Dk = 2Hk tan(θk )
i=k −2αdi
Uk = Rk,k+1 Πi=1 Ti−1i Tii−1 e
1
Tco = (T + T⊥ )
2
1
Rcross = (R − R⊥ )
2
2π √
α= |Ima{ }|
λ

14. Introduction Model Results obtained Conclusions
Methodology
Input of the forward model (MLSR)
Depths and permittivity of the dry snow layers are needed
Retrieved from in situ measurements of snow density

15. Introduction Model Results obtained Conclusions
Methodology
Complex waveform generated
Incident signal at surface with A=1
Direct signal set to lag 22 (RHCP to
LHCP leakage with A=0.1)
Frequency of direct signal as a
reference
Several contributions

16. Introduction Model Results obtained Conclusions
Methodology
Complex waveform generated
Incident signal at surface with A=1 Example: elevation from 44.884 to 44.955
Direct signal set to lag 22 (RHCP to deg (128 samples)
LHCP leakage with A=0.1)
Frequency of direct signal as a
reference
Several contributions

17. Introduction Model Results obtained Conclusions
Methodology
Comparison of the modeled waveforms with real data

18. Introduction Model Results obtained Conclusions
Methodology
Comparison of the modeled waveforms with real data

19. Introduction Model Results obtained Conclusions
Methodology
Evolution of the different contributions wrt incidence angle
⇒ Interferometric frequency relates to depth of the layer

20. Introduction Model Results obtained Conclusions
Methodology
How do we retrieve information?
FFT to each of the lag-time series ⇒ elevation domain (cycles/deg)
Several bands of main contributions below the surface level appear,
corresponding to depths with stronger gradients of snow density/permittivity
⇒ Proper inversion might determine dominant layers of L-band reflections
300
Lag-hologram from previous example
Snow Depth (m)
200
100
0
−18 −15 −12 −9 −6
Interf. Freq. (cycles/deg−el)

21. Introduction Model Results obtained Conclusions
Outline
1 Introduction
2 Model
3 Results obtained
4 Conclusions

22. Introduction Model Results obtained Conclusions
Lag-holograms from real data
Lag-hologram of 256 samples
PRN 19 at ∼ 40◦ of elevation from Dec-16.
First impressions
It show assymetrical behavior: consistent
with rotation due to interference from
different contributions.
Apparently, wider frequency fringes than
expected (high frequency bands at short
delay lags).
Next processing step: averaging
To fade away those other features of the data which are not consistently
repeated (noise, atmospheric and instrumental induced features).
To identify the geometric and experimental parameters which essentially drive
the interferometric signal.

23. Introduction Model Results obtained Conclusions
Averaging in elevation
5◦ - 10◦ 10◦ - 15◦
Frequency (cycle/deg−elev.)
Frequency (cycle/deg−elev.)
Next slides show a series of 20 20
15 15
averaged lag-holograms
10 10
(using all PRN’s) in 5 5
elevation steps of 5◦ from 0 0
−5 −5
December 16th. −10 −10
−15 −15
−20 −20
5◦ ⇒ 65◦ 10 20 30 40 50 60 10 20 30 40 50 60
Delay−lag (15 m.−lag) Delay−lag (15 m.−lag)

24. Introduction Model Results obtained Conclusions
Averaging in elevation
15◦ - 20◦ 20◦ - 25◦ 25◦ - 30◦
Frequency (cycle/deg−elev.)
Frequency (cycle/deg−elev.)
Frequency (cycle/deg−elev.)
20 20 20
15 15 15
10 10 10
5 5 5
0 0 0
−5 −5 −5
−10 −10 −10
−15 −15 −15
−20 −20 −20
10 20 30 40 50 60 10 20 30 40 50 60 10 20 30 40 50 60
Delay−lag (15 m.−lag) Delay−lag (15 m.−lag) Delay−lag (15 m.−lag)

25. Introduction Model Results obtained Conclusions
Averaging in elevation
30◦ - 35◦ 35◦ - 40◦ 40◦ - 45◦
Frequency (cycle/deg−elev.)
Frequency (cycle/deg−elev.)
Frequency (cycle/deg−elev.)
20 20 20
15 15 15
10 10 10
5 5 5
0 0 0
−5 −5 −5
−10 −10 −10
−15 −15 −15
−20 −20 −20
10 20 30 40 50 60 10 20 30 40 50 60 10 20 30 40 50 60
Delay−lag (15 m.−lag) Delay−lag (15 m.−lag) Delay−lag (15 m.−lag)

26. Introduction Model Results obtained Conclusions
Averaging in elevation
45◦ - 50◦ 50◦ - 55◦ 55◦ - 60◦
Frequency (cycle/deg−elev.)
Frequency (cycle/deg−elev.)
Frequency (cycle/deg−elev.)
20 20 20
15 15 15
10 10 10
5 5 5
0 0 0
−5 −5 −5
−10 −10 −10
−15 −15 −15
−20 −20 −20
10 20 30 40 50 60 10 20 30 40 50 60 10 20 30 40 50 60
Delay−lag (15 m.−lag) Delay−lag (15 m.−lag) Delay−lag (15 m.−lag)

27. Introduction Model Results obtained Conclusions
Averaging in elevation
55◦ - 60◦ 60◦ - 65◦ Apparently, the elevation
range that shows consistent
Frequency (cycle/deg−elev.)
Frequency (cycle/deg−elev.)
20 20
15 15
features from deep snow
10 10
5 5 layers goes from 20◦ to
0 0
45◦ .
−5 −5
−10 −10
−15 −15 The elevation-rate also
−20 −20
10 20 30 40 50 60 10 20 30 40 50 60 plays an important role in
Delay−lag (15 m.−lag) Delay−lag (15 m.−lag)
this analysis.

28. Introduction Model Results obtained Conclusions
Averaging in elevation-rate
0.0◦ /s - 0.001◦ /s 0.001◦ /s - 0.002◦ /s
Next slides show a series of
Frequency (cycle/deg−elev.)
Frequency (cycle/deg−elev.)
20 20
averaged lag-holograms 15 15
(using all PRN’s) in 10 10
5 5
elevation-rate steps of
0 0
0.001◦ /s from December −5 −5
−10 −10
16th.
−15 −15
−20 −20
10 20 30 40 50 60 10 20 30 40 50 60
0.001◦ /s ⇒ 0.008◦ /s Delay−lag (15 m.−lag) Delay−lag (15 m.−lag)

29. Introduction Model Results obtained Conclusions
Averaging in elevation-rate
0.002◦ /s - 0.003◦ /s 0.003◦ /s - 0.004◦ /s 0.004◦ /s - 0.005◦ /s
Frequency (cycle/deg−elev.)
Frequency (cycle/deg−elev.)
Frequency (cycle/deg−elev.)
20 20 20
15 15 15
10 10 10
5 5 5
0 0 0
−5 −5 −5
−10 −10 −10
−15 −15 −15
−20 −20 −20
10 20 30 40 50 60 10 20 30 40 50 60 10 20 30 40 50 60
Delay−lag (15 m.−lag) Delay−lag (15 m.−lag) Delay−lag (15 m.−lag)

30. Introduction Model Results obtained Conclusions
Averaging in elevation-rate
0.005◦ /s - 0.006◦ /s 0.006◦ /s - 0.007◦ /s 0.007◦ /s - 0.008◦ /s
Frequency (cycle/deg−elev.)
Frequency (cycle/deg−elev.)
Frequency (cycle/deg−elev.)
20 20 20
15 15 15
10 10 10
5 5 5
0 0 0
−5 −5 −5
−10 −10 −10
−15 −15 −15
−20 −20 −20
10 20 30 40 50 60 10 20 30 40 50 60 10 20 30 40 50 60
Delay−lag (15 m.−lag) Delay−lag (15 m.−lag) Delay−lag (15 m.−lag)

31. Introduction Model Results obtained Conclusions
Averaging in elevation-rate
Consistent features from
0.006◦ /s - 0.007◦ /s 0.007◦ /s - 0.008◦ /s deep snow layers are shown
from up to ∼0.005◦ /s.
Frequency (cycle/deg−elev.)
Frequency (cycle/deg−elev.)
20 20
15 15
10 10
5 5 Expected result:
0 0
interferometric information
−5 −5
−10 −10
depends on the evolution of
−15 −15 the different paths followed
−20 −20
10 20 30 40 50 60 10 20 30 40 50 60 by each layer-contribution
Delay−lag (15 m.−lag) Delay−lag (15 m.−lag)
during the time-series of
data (fixed).

32. Introduction Model Results obtained Conclusions
First conclusions from averaging
A minimum elevation and elevation-rate are needed for obtaining persistent
features in the lag-holograms.
The apparently bad results at higher elevations may be due to the impact of low
elevation-rate samples in the elevation averaging.
Test: Data set divided in cells of elevation and elevation-rate ⇒ Averaging over
most populated cell.
0.008
Cell division
Elevation rate (deg−elev/s)
30
Counts
Elevation rate (deg−elev/s)
0.006 25 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70
20 0.008
PRN
0.004
15 0.006
10 0.004
0.002
5
0.002
0.000
10 20 30 40 50 60 70 0.000
10 20 30 40 50 60 70
Elevation angle (deg)
Elevation angle (deg)

33. Introduction Model Results obtained Conclusions
Averaging in cell: Repeatability
Dec 16th Dec 17th
Frequency (cycle/deg−elev.)
Frequency (cycle/deg−elev.)
20 20
15 15
10 10
5 5
0 0
−5 −5
−10 −10
−15 −15
−20 −20
10 20 30 40 50 60 10 20 30 40 50 60
Delay−lag (15 m.−lag) Delay−lag (15 m.−lag)
Dec 18th Dec 19th
Frequency (cycle/deg−elev.)
Frequency (cycle/deg−elev.)
20 20
15 15
10 10
5 5
0 0
−5 −5
−10 −10
−15 −15
−20 −20
10 20 30 40 50 60 10 20 30 40 50 60
Delay−lag (15 m.−lag) Delay−lag (15 m.−lag)

34. Introduction Model Results obtained Conclusions
Depth of the contributing layers
Most of the reflected signals comes from MODEL
first 40 meters: especially 10 first meters
–5 to 7 cycle/deg–, and from 30 to 40
meters depth –around 9 cycle/deg–.
Remarkable contributions between 75 and
100 meters –10 to 12 cycle/deg–, and
around 110 and 140 meters –14 and 16
cycle/deg–.
Layers corresponding to depths with
stronger gradients of snow
density/permittivity from the in-situ
measurements. DATA (averaged cell)
300
Snow Depth (m)
200
100
0
−18 −15 −12 −9 −6
Interf. Freq. (cycles/deg−el)

35. Introduction Model Results obtained Conclusions
Outline
1 Introduction
2 Model
3 Results obtained
4 Conclusions

36. Introduction Model Results obtained Conclusions
Conclusions
Persistent signatures have been found in the collected data-set of GPS
reflections over dry snow.
The frequency-domain analysis shows interferometric behavior
(asymmetrical spectrum) with contributions below the snow surface level.
No success when attempting a total inversion of the dry snow layers
profile from the data.
In spite of the poor results, the link between frequency bands in the
lag-holograms and the depth of a reflecting interface is still a source of
information.
Alternative estimates
In [Hawley et al., 2006], the delays of radar measurements are not used to
estimate the snow density, but combined with a given density profile to
estimate the snow accumulation rates. A similar application can be
envisaged for this data set.

37. Introduction Model Results obtained Conclusions
Thank you for your attention

38. Introduction Model Results obtained Conclusions
References
Macelloni et al., 2006: G. Macelloni et al., ”DOMEX 2004: An Experimental Campaign at Dome-C
Antarctica for the Calibration of Spaceborne Low-Frequency Microwave Radiometers”, IEEE Trans. Geosci.
and Remote Sens., vol. 44, 2006.
Wiehl et al., 2003: M. Wiehl, R. Legresy, and R. Dietrich, ”Potential of reflected GNSS signals for ice
sheet remote sensing”, Progress in Electromagnetics Research, vol. 40, pp. 177–205, 2003.
Hawley et al., 2010: R.L. Hawley, E. M. Morris, R. Cullen, U. Nixdorf, A. P. Shepherd and D. J.
Wingham, ”ASIRAS airborne radar resolves internal annual layers in the dry-snow zone of Greenland”,
Geophysical Research Letters, vol. 33, 2006.