Polarimetric and Interferometric Methods to Determine Snow ...seom.esa.int/polinsar-biomass2015/files/D3S3_Cryosphere...Polarimetric and Interferometric Methods to Determine Snow Depth,
Post on 24-Jul-2020
1 Views
Preview:
Transcript
Polarimetric and Interferometric Methods to Determine Snow Depth, SWE, and the
Depth of Fresh Snow
Silvan Leinss, Andreas Wiesmann, Juha Lemmetyinen, Giuseppe Parrella, Irena Hajnsek
28th January, 2015
Definition & Motivation
Snow-Water-Equivalent 20 mm (SWE)
water column
+15
cm Fresh Snow
Depth
100
cm
Snow Height
2
Snow structure
Hydrology / Run-off models
Traffic
Risk Management (Avalanches, Flooding)
Climate
Weather Forecast
Vegetation
Rodents / Lemmings
Three Different Phase Differences Snow-Water-Equivalent
20 mm SWE water column
Differential Phase (repeat pass)
3
Interferometric Phase (single pass) 10
0 cm
Snow Height
Polarimetric Phase (Polarimetry)
+15
cm Fresh Snow
Snow structure
4
5
Propagation Delay due to Dry Snow
∆Zs ε(ρ)
snow
• N.B.: ∆φ can be summed for layers of different density ρ (due to Snell‘s law).
ε(ρ) = permittivity of snow (density dependent) ∆Z = Snow Depth
∆R = 2 ∙ (∆R0,air – (∆Rair + nsnow∙∆Rs) )
two-way path difference snow free – snow covered:
Refractive index: nsnow = ε 2
Two way phase difference (D-InSAR)
λ0 = Radar wave length in free space θ0 = radar incidence angle
θ0
air
P common point Guneriussen (2001), TGRS vol. 39
• Assumption: Low scattering at snow interfaces and in the volume.
Differential Phase ∆φ: a Linear Function of SWE
6
ξ = 0.1 … 0.5 for seasonal snow
∆φ = 2π -> 18 mm SWE
• High Sensitivity: Phase wrapping at 5 – 10 cm of snow at X-Band
∆φ ≈ 2π / λ ∙ (1.59 + θinc5/2 ) ∙ ∆SWE
Valid for all snow densities, θinc < 60°
• Differential phase can be well approximated:
∆SWE = ρ ⋅ ∆Z
Problems of D-InSAR
7 TSX: differential interferograms, ∆t = 11 days
Strong loss of coherence in X-band
Atmospheric phase delays on the order of 2π
+ Phase wrapping.
Almost impossible to get reasonable snow data from differential interferograms. except: for very fast acquisitions rates! -> SnowScat instrument.
SnowScat: Fully Polarimetric Coherent Real Aperture Radar (RAR). Acquisition rate: 4 hours. Frequency: 9.2 … 17.8 GHz Observation: 17 subsectors (sect. 1), 4 incidence angles
the SnowScat Instrument
8 Test site: Finland, Sodankylae
SnowScat: 4 hours „Multi-Pass“ Coherence
• Coherence γ4h > 0.99 for dry snow. • Wet snow: γ4h ≈ 0.3 ..0.7 • -> very reliable differential phase measurements.
9
Dry snow season Snow melt
Sum of Differential Interferograms
∆Φs(t, t0) = Σ∆φsignal + Σ∆φfluct
10
In a sum of (phase) differences, all noise & systematic fluctuations cancel out:
3rd interf. 2nd interf. 1st interf.
= 0 = 0
Invert total phase to get total SWE:
1st acquisition
2nd acquisition 3rd acquisition 2nd acquisition
Only the phase error of the first and last acquisition remains.
Σ∆φfluct = φfluct (t4) - φfluct (t1)
Σ∆φsignal= φsignal (t4) - φsignal (t1) (total phase ∆Φs is unwrapped!)
- φfluct (t3) + φfluct (t3) - φfluct (t2) + φfluct (t2)
Results: SWE Determination @ 10 and 16 GHz
11
Leinss (2015), JSTARS submitted.
Results: • RMSE of 5 mm (total SWE: 200 mm) • No saturation at high SWE • No frequency dependence • Volume scattering can be neglected @
16 GHz! (for seasonal Finnish snow.)
if TanDEM-X would be a multipass system, -> DEM height error up to 1000 m !!
200 mm SWE = 10 – 30 phase cycles!
Year 1
Year 2
Year 3
Year 4
Gray: Time series of 68 subsectors
TanDEM-X: Single Pass Interferometry
θ0
R0
TanDEM-X
B⊥
13
∆θ
∆z
Phase error in single pass interferometry:
= 0.0004 for B⊥ = 2000m (∆θ = 0.2°)
-> 10 km deep dry snow for one single phase cycle.
Wet snow: low penetration -> DEM differencing
(single pass)
-> No DEM error due to dry snow.
InSAR phase difference, bistatic
Destinguish dry and wet snow by backscatter signal. kz
Dry vs. Wet Snow
2013-04-06 Dry snow 2013-04-17 Wet snow 14
Significantly decreasing backscatter signal TDX, Aletschgletscher, Switzerland
2013-04-06 Dry snow 2013-04-17 Wet snow
Snow Accumulation by DEM Differencing
15
DEM Difference
Snow depth data, SLF
Differential Phase & Interferometric Phase Snow-Water-Equivalent
of dry snow water column
Differential Interferometry (repeat pass)
16
Single pass Interferomety
100
cm Wet snow depth
+15
cm
Polarimetric Phase
(dry snow not detectable!)
Copolar Phase Difference (CPD): ∆φ = φVV - φHH
„Why this correlation“? (Leinss, PolInSAR 2013)
17
Spatial correlation (TerraSAR-X)
January 2012
CPD Sensitivity to Fresh Snow
18
TerraSAR-X
Fresh Snow Depth = f(∆CPD)
∆φCPD = +15° / 11 days per 10 cm fresh snow in X-Band
19
∆φCPD = -5° / 11 days during cold temperatures
Leinss (2014), JSTARS, vol. 7
Depth of fresh snow can be estimated from the polarimetric phase difference φVV – φHH.
Riche (2013), J. Glaciology, vol. 59
CPD and Anisotropy of Snow
20
Fresh snow: horizontal structures Metamorphic snow: isotropic -> vertical structures
Effect of structural anisotropy can be modeled using the Maxwell-Garnett theory. Sihvola (2000), Subsurface Sensor Technol. Appl., vol. 1 Sihvola (2002), TGRS ,vol. 40 Leinss (2014), JSTARS vol. 7 Result:
εH > εV for horizontal structures (φVV - φHH > 0) εV > εH for vertical structures (φVV - φHH < 0)
Phase difference between VV and HH polarization:
(BSA)
Copolar Phase Difference (CPD): ∆φ = φVV - φHH
„Why this correlation“?
(Leinss, PolInSAR 2013)
21 = 0.02 for | εV – εH | = 0.05 100 cm snow -> ∆φ ≈ 2π (10 GHz)
(Fujita, J. Glaciology 2014)
Consider snow as a birefringent medium
V H Spatial correlation
(TerraSAR-X)
Compare TSX with SnowScat
22
θ = 32.7°
April Nov Dec Jan Feb Mar
∆t = 11 d
∆t = 4 h
SnowScat shows same result, but with > 50x better temporal resolution
Snow Metamorphism: CPD = f (SD, Tair)
23
Vertical structures grow in the whole snow volume (SD) driven by a temperature gradient Tair / SD.
Settling fresh snow (∂t SD) causes increasingly horizontal structures which build up within time ( e -t/τ ).
d/dt
Summary Snow-Water-Equivalent
of dry snow water column
Differential Interferometry (repeat pass)
24
Single pass Interferomety
100
cm Wet snow depth
Polarimetry of birefringent media
(dry snow not detectable!)
Model: φVV - φHH = f (SnowDepth, Tair)
+15
cm Fresh Snow depth
Anisotropy
Absorption and Scattering losses in Snow
26
Mv = volumetric water content Pex = Exponential correlation coefficient of snow structure ( ~grain size)
2-frequency phase unwrapping:
28
Wrapped phase cycles can be recovered using a dual-frequency approach.
Phase measured with frequency A
Phas
e m
easu
red
with
freq
uenc
y B
Leinss, JSTARS 2015 (submitted)
Polarization Dependence: Differential Interferometry
29
TanDEM-X Snow Penetration
30
Apr. 06
Apr. 17, 28.
Maxwell-Garnett-Theory
31 Effect is maximal at a snow density of 0.2..0.4, where no dependence on density exits. -> Snow Depth determination, but no SWE.
∆ζ
32
Fujita, J. Glaciology (2014)
top related