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)