READING AND MODELLING
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Transcript of READING AND MODELLING
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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
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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
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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
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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)
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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
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LANDSAT 7orbit repeated after 16 days
COVERAGE
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SARINTERFERO-
METRY
1) velocity field
2) topography
InSAR
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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 !
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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)
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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
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RAW INTERFEROGRAM
Contours (colours) connecting points of equal phase difference are called fringes
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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
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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
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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
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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
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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
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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
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DETECTING GLACIER FACIES
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GLACIER FACIES
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SNOW LINE FROM NEAR-INFRARED IMAGERY
Morteratschgletscher
TM band 4 (800 - 900
nm)
24 June 1999
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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!
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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
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AN EXAMPLE: FACIES ON KONGSVEGEN (SVALBARD) FROM SAR
1-4ice
5-6supimp.ice
8-9snow
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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
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RADAR ALTIMETRY: RANGE RESOLUTION
H = 0.5 c tp
H ≈ 0.5 m
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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”)
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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
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CHANGE IN ELEVATIONAT CROSSING POINTS
Only at crossing point of ascending and descending tracks, because repeat tracks are too far apart (a few km)
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ELEVATION CHANGE ANTARCTICA
Period: 1992 - 1996
No orbits beyond
about 81 ˚S
Only measurements
when slope < 1˚
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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
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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
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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)
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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.
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SIGNALS ARE AVERAGED
for ERS-1 over 50 returnsReal frequency: 20 HzDistance of info along track = 330 m
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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
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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
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PULSE REPETITION FREQUENCY
For ERS-1: 1 kHzPulses are 10-3 s apart, compare to pulse duration of 3 ns
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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
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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
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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
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ATMOSPHERIC WINDOWS
AVHRR bands 4 and 5 are situated in the atmospheric window between 10.3 and 12.5 µm
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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:
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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 !