READING AND MODELLING

Review about mass balance modelling:

Greuell, W., and C. Genthon, 2004: Modelling land-ice surface

mass balance. In Bamber, J.L. and A.J. Payne, eds. Mass

balance of the cryosphere: observations and modelling of

contemporary and future changes. Cambridge University

Press.

Mass balance model that includes sub-surface module:

http://www.phys.uu.nl/%7Egreuell/massbalmodel.html

Karthaus, September 2005

Wouter Greuell

Institute for Marine and Atmospheric Research Utrecht (IMAU)Utrecht University, the Netherlands

Retrieval of: - surface

velocity

- surface

topography

- glacier facies

- surface albedo

REMOTE SENSING OF GLACIERS

WAVE LENGTHS AND RETRIEVABLE INFORMATIONGlaciology

0.1 1 10 100 1000 104 105 106

Intensity

Wave length (µm)

ultraviolet

long-wave:emitted byatmosphereand surfaceof the Earth

short-wave:emitted by Sun

albedoglacier facies

surface topographysurface

temperature

Terms inmeteorology

Retrievableinformationblue: active

green: passive

optical sensors microwave sensors (e.g. radar)

visiblenear infraredmid infraredthermal infrared microwaves (e.g. radar bands)

surface velocityglacier facies

surface topography

Types of radiation (physics)

Types of sensors

X-band L-bandC-band

Frequency (GHz)

30 0.3300 3300000 30000 3000

altitude = 705 km

inclination = 98˚

No data beyond 82 ˚N and S

orbit period = 99 min

ground-track speed ~ 6.7

km/s

crosses equator at 9:45 AM

local time (for optical

sensors)

ORBIT (LANDSAT 7)

LANDSAT TM (1,

2 and 3)

total field of view: 11.6˚

scan mirror oscillates

once per 33 msec

6 detectors per band i.e.

six contiguous lines

for each mirror

semi-oscillation

SCANS

LANDSAT 7orbit repeated after 16 days

COVERAGE

SARINTERFERO-

METRY

1) velocity field

2) topography

InSAR

SIDE-LOOKING RADAR(REAL-APERTURE RADAR)

Rr =ctp2sinθ

if tp = 30 ns, = 35˚ then Rr = 8 m

Emission of a short pulse: tp = 30 ns

Across-track resolution obtained by time-resolving the signal

Along-track resolution is poor

Ra=Hλ

L cosθ

if H = 800 km, = 24 cm, L = 10 m= 35˚ then Ra = 24 km

Activesensor !

SYNTHETIC APERTURE RADAR (SAR)

Increase along track resolution

computer time-demanding procedure (called focusing) with complex numbers

pulse repetition frequency: 1000 Hz

satellite speed: 6 km s-1

Every 6 m a sample is taken

Every measurement contains the information from 4000 ground elements of 6 m, but each ground

element is sampled 4000 times ......

Therefore, 4000 measurements are taken within24 km (the original along-track resolution)

PRINCIPLE OF SAR INTERFEROMETRY

- Use 2 images (A and B) from repeat orbits (typically no more than a few 100 m apart = d)

- Use phase ()- Range (R; distance satellite to

pixel) = n (integer number) * (6 cm) + /2 *

- So phase gives some info about range (but n is unknown!)

- Take difference of phases from two images for each pixel = difference in range from two orbits ( but (nA-nB) is unknown!)

- Make image of phase difference (= interferogram)

Orbit AImage A

Orbit BImage B

d

€

RA = nAλ +φB

2πλ

€

RB = nBλ +φB

2πλ

Contributions to interferometric signal:- Differences in positions orbits- Surface topography- Surface displacements

pixel i pixel i+1

RAW INTERFEROGRAM

Contours (colours) connecting points of equal phase difference are called fringes

THE INTERFEROMETRIC LIMIT

Targets must remain stable between image acquisitions (e.g. 3 days)

phase from pixel is random

is removed by differencing two signals from the same pixel

Pixel must not stretch or shrink by more than a fraction of from one image to the other

2 L ( sin 1 - sin 2 ) <

orbital separation (d) should be < 1 km

signal from a pixel is the sum of hundreds of elementary targets

L

1 pixel

1

dR 1=2Lsin1

if d too large: incoherence

dR = differencein path length for extreme

ends of one pixel

ALTITUDE OF AMBIGUITY

= shift in altitude of the surface corresponding to a phase shift of 2π in the interferogram

ha: altitude of ambiguityR: range from satellite to target: wavelength: angle of incidenced: horizontal separation of trajectories

If interested in topography: large dIf interested in displacements: small d

€

ha =Rλ

2dtanθ

d

ha

R

DIGITAL ELEVATION MODEL

Note: phase needs to be unwrapped. Tie points needed!

glacier free terrain in Alaska

prior (a) and after (b) removal of orbital effect

a b

SEPARATE VELOCITY FROM TOPOGRAPHIC

FIELD

Option 1: create synthetic

interferogram from known topography

and und subtract this from measured

interferogram

Option 2:

differential

interferometry:

use two

interferograms and

assume constant

velocity

Day 1

Day 4

altitude of ambiguityha1

ψ1

(topographyh 1a )+

velocity

Images Interferograms

16Day

19Day

altitude of ambiguityh 2a

ψ2

(topographyh 2a )+

velocity

Differentialinterferograms

ψ12

topographyonly

becauseh 1a differs fromh 2a

ψ1−12

velocity only

ψ2−12

velocity only

EXAMPLE OF

VELOCITY FIELD

Bagley Ice FieldAlaska

a) Date 1: topography

(h) and velocity (v)

b) Date 2: h + v

c) h only

d) Date 2: v only

ESTIMATE SURFACE VELOCITY

Limitation!Calculated velocity = velocity

along line connecting the target with the satellite

Extra info:- another interferogram- assume surface parallel flow- assume flow along the

surface gradient- assume flow along valley

walls

DETECTING GLACIER FACIES

GLACIER FACIES

SNOW LINE FROM NEAR-INFRARED IMAGERY

Morteratschgletscher

TM band 4 (800 - 900

nm)

24 June 1999

EFFECTS ON THE RADAR SIGNAL = 3 -25 cm

incidenceangle (20 - 50˚)

satellitesensor

rough surface(Δh > 1 cm):

smooth surface(Δh < 1 cm):

elements < 1 cm:

elements > 1 cm: do

by ice (absorption length = 10 m):

by water (absorption length = 5 mm):

amplitude!

Atmosphere some absorption by clouds with water droplets, but no scattering

All images useful

Water in snow or on ice strong absorption use winter images

Most glacier surfaces are rough

backscattered signal depends on shape of roughness elements

Volume scattering increases with concentration of large ( > 1 cm ) inhomogeneities

Facies Large

inhomogeneities

Signal

dry-snow few weak

wet snow and percolation grain clusters and ice lenses strong

ice (transformed from snow) some air bubbles and cracks medium

superimposed ice more air bubbles between strong and medium

THE RESULTING RADAR SIGNAL

AN EXAMPLE: FACIES ON KONGSVEGEN (SVALBARD) FROM SAR

1-4ice

5-6supimp.ice

8-9snow

RADAR ALTIMETRY (PRINCIPLE)

Principle: - emittance of a short (tp = 3 ns)

pulse

- detection of the return

- determination of the travel time

(Tt)

- calculation of the distance to the

surface (H)H=

Ttc2

RADAR ALTIMETRY: RANGE RESOLUTION

H = 0.5 c tp

H ≈ 0.5 m

RADAR ALTIMETRY: FOOTPRINT

Footprint (x) = diameter of circle when rear front hits surface

€

H2 + 0.5 x( )2

= H + ct p( )2

From H >> ctp, it follows:

€

€

x = 8ct pH x ≈ 2400 m

The footprint is “pulse-limited” (and not “beam limited”)

SLOPE-INDUCED ERROR

α

true terrain surface

platform motionR1 R2

S1

S2S1

S2

apparent terrain surface

H1 H1

H2 H2

Technique works only when slope < 1 degree

CHANGE IN ELEVATIONAT CROSSING POINTS

Only at crossing point of ascending and descending tracks, because repeat tracks are too far apart (a few km)

ELEVATION CHANGE ANTARCTICA

Period: 1992 - 1996

No orbits beyond

about 81 ˚S

Only measurements

when slope < 1˚

ELEVATION CHANGE WITH AIRBORNE LASER

Same principle as radar altimeter, but:

- flight lines are repeated exactly, leading

to info along entire flight lines

- Footprint ≈ 1 m

- Direction of reflection known with large

accuracy (no problem over steep terrain)

but

- Total length of flight lines limited

Elevation changes Greenland 1997-2003

TOPOGRAPHY FROM RADAR, LASER AND SAR

Radar on board ENVISAT

Laser on board ICESat

SAR interferometry

Wavelength (nm) 2.2 and 9.4 cm 530 and 1060 nm 3 - 24 cm

Spatial resolution1.7 - 2.4 km

pulse-limited

70 m

beam-limited80 m

Range resolution 5 - 20 cm 10 cm 5 - 20 m

Can be used if slope > 1˚

no yes yes

Penetrates through clouds

yes no yes

Useful for big ice sheets

yes yes tie points needed

Product after one flight line

1D 1D 2D

SUM UP

1) Orbits, swath, resolution

2) SAR interferometry for surface velocity and

topography

3) Glacier facies with optical sensors and SAR

4) Altimetry with radar (laser and SAR)

SOME READING

Introduction to remote sensing:

Rees, W.G., 2001: Physical principles of remote sensing. Cambridge University

Press, Cambridge (U.K.), 343 pp.

Review about remote sensing of snow and ice:

König, M., J.-G. Winther and E. Isaksson, 2001: Measuring snow and glacier

properties from satellite. Rev. Geophys., 39 (1), 1-27.

Review about SAR interferometry:

D. Massonnet and K. L. Feigl, 1998: Radar interferometry and its application to

changes in the Earth’s surface. Rev. Geophys., 36 (4), 441-500.

Paper about using SAR interferometry to derive glacier velocity field:

Fatland, D.R. and C.S. Lingle, 1998: Analysis of the 1993-95 Bering Glacier (Alaska)

surge using differential SAR interferometry. J. Glaciol., 44 (148),532-546.

SIGNALS ARE AVERAGED

for ERS-1 over 50 returnsReal frequency: 20 HzDistance of info along track = 330 m

RANGE WINDOW

Signal is sampled within short time interval (relative to pulse repetition time) in order to reduce data volume = range window

Half-power point = retrack point = mean surface elevation within footprint for Gaussian distribution of slopes

Onboard tracker tries to predict travel time of next return in order to place range window correctly

When signal is missed altogether: loss of lock

Sensor goes into “acquisition mode”: no data for a few seconds

MEASURED RETURN SIGNALS

- every signal is mean of 50 returns- every sixth signal is shown- flight over margin Greenland ice

sheet- 40-48: coast- 106-232: loss of lock in rugged

terrain- 238-274: ice sheet

PULSE REPETITION FREQUENCY

For ERS-1: 1 kHzPulses are 10-3 s apart, compare to pulse duration of 3 ns

ERROR SOURCES

Relevant for changes in ice-elevation measurements:- Atmospheric

a) dry atmosphereb) wet atmospherec) ionosphere

- Orbit- Variation in sub-surface properties (from which depth is the signal

reflected?)- Slope (see next slide)

Note also that changes in snow (ice) density without changes in elevation do not affect volume, but they do affect mass and sea level

DETERMINATION OF THE SURFACE TEMPERATUREBLACK-BODY RADIATION

0

0.2

0.4

0.6

0.8

1

5 10 15 20 25 30 35 40

Normalized (300 K) radiance

Wavelength (µm)

250 K

275 K300 K

Band of measurement

BRIGHTNESS TEMPERATURE

This temperature is called the brightness temperature

Satellite sensors are calibrated on-board with blackbodies of known temperatures

The real surface temperature is several degrees centigrade higher than the brightness temperature due to absorption in the atmosphere

ATMOSPHERIC WINDOWS

AVHRR bands 4 and 5 are situated in the atmospheric window between 10.3 and 12.5 µm

SPLIT WINDOW AND DUAL VIEW

Ts = a0 + a1 TB1 + a2 TB2

where Ts: surface temperature

ai: constants

TBi: brightness temperatures obtained from different sensors

Split window: brightness temperatures from two different spectral bands

Dual view: brightness temperatures from two different angles

Equation optimized by means of measurements or calculations

Difference real surface - brightness temperature varies with:

amount of greenhouse gases along atmospheric path- concentration of gases (e.g. water vapour)- surface elevation

If this is unknown:

SAR INTERFEROMETRY= differencing the phases of two SAR images

phase = range = distance between satellite and ground target

difference in phase = difference in range (between 2 images)

Contributions to interferometric

signal:- differences in orbital trajectories- surface topography- surface displacements

φ= 0

φ = π

φ = 1.5 π

is not absolute, but relative !