Advanced Optical Theory - 2 Retrieval of...

Advanced Optical Theory - 2Retrieval of Information

Jose Moreno

3 September 2007, Lecture D1La5

3 September 2007 D1La5 Advanced Optical – Retrieval of Information Jose Moreno 2

ADVANCED OPTICAL THEORYPart II: Retrieval of information

Information content of optical data in spectral and angular domains

Forward modelling of surface reflectance: soil, leaf and canopy models

Information retrieval based on optimised spectral indices

Information retrieval based on model inversion techniques

Advanced retrieval techniques: multi-step procedures

Validation of retrievals

Scaling issues

Information content ofoptical data in the spectal

and angular domains

MERIS Landsat TM

HyMapCHRIS

250023002100190017001500130011009007005003003000

wavelength (nm)

WATER ABSORPTION

CHLOROPHYLL ABSORPTION

250023002100190017001500130011009007005003003000 . 0 0

0 . 0 1

0 . 0 2

0 . 0 3

0 . 0 4

0 . 0 5

0 . 0 6

0 . 0 7

0 . 0 8

wavelength (nm)

LAI fCoverTH

l iqu id w at er abs orp tion b ands

hot-s pot eff ect

v iew angle (principal p lane)

w av elength

chlorop hy ll abs orp tion

Sun z enith angle

Sensor scan

0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.60

wavelength ( m)

cegreen vegetation (alfalfa)senescent vegetation (barley)

DAISEX-1999Barrax / HyMap data /

Hot-Spot Target

Sensor

Hot-Spot Target

Optimised observation geometry: - flight time and flight direction - maximum solar elevation angle High radiometric sensitivity

SouthNorth

- several view angles at maximum solar elevation- several flights af different solar elevations- maximisation of angular range (hot-spot and dark-spot)

Planning experiments to test angular information

400 600 800 1000 1200 1400 1600 1800 2000 2200 2400 2600

SUGAR BEET

wavelength (nm)

ALFALFA

Line 1 , noonLine 2 , noonLine 1 , morningLine 2 , morningLine 1 , af t ernoonLine 2 , af te rnoon

SV6 - C03 UTM-X: 577783 UTM-Y: 4324794 LAI = 1.71 fCover = 0.61

Line 1 , noonLine 2 , noonLine 1 , morningLine 2 , morningLine 1 , af t ernoonLine 2 , af te rnoon

V16 - C01 UTM-X: 577550 UTM-Y: 4324069 LAI = 1.84 fCover = 0.95 Hyperspectral versus

directional information

A rather Lambertian surface

A highly anysotropic surface

POLDER dataDAISEX-99 / Barrax, Spain

0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95

wavelength (μm)

POLDER spectral channels

multiangular coverage

Four flights, different solar elevations: - early morning - mid-morning - noon - afternoon Simultaneous with HYMAP and DAIS data

specular

POLDER data

Irrigated alfalfa field

Channel 3 (550 nm)

POLDERnoon flight

POLDERmorning flight

3º - 10º

6º - 20º

20º - 45º

Angular effects are especially critical for airborne data

Daedalus campaignEvora, Portugal

13 m/pixel (nominal) – image: 1 m/pixel

--33ºº --11ºº 11ºº 33ºº 55ºº 88ºº

3.6 m/pixel (nominal) – image: 1 m/pixel

--55ºº 33ºº 1010ºº 1818ºº 2424ºº 3232ºº

1.5 m/pixel (nominal) – image: 1 m/pixel

--3838ºº --2323ºº --88ºº 1010ºº 2424ºº 4040ºº

Daedalus campaignEvora, Portugal

Angular effects versusspatial resolution

MISRTerra

Beginimaging

Endimaging

Line-of-sightof imager

Image2Image4Image5 Image1Image3

Scanning speed = 1/5 of spacecraft ground speed

CHRIS / PROBA

62 spectral bands34 m resolution5 view angles

CHRIS/PROBA DATA

Forward modelling of surface reflectance:

soil, leaf and canopy models

FORWARD MODELLINGLeaf Canopy Environment

Soil / LitterWater /Snowbackground

BARE SOILREFLECTANCE

only top soilis relevant

Hapke (1981) bidirectional reflectance model

ACTUAL DATA (HYMAP)

shadow-hiding mechanismreflections and refractions throughsurfaces and insidethe particle volume(coherent scattering)

opposition effect

LEAF MODEL

- Must account for reflectance andtransmitance of the leaves

- Explicit description of spectral variations

- Explicit description of angular effectsin both reflectance and transmittance

- Accountig for fluorescence emission

SEVERAL MODELS AVAILABLE, BUT NONE IS DESCRIBING ALL THE EFFECTSIN A PROPER WAY (USER MUSTCHOOSE WHICH EFFECTS ARE MORERELEVANT FOR A GIVEN APPLICATION)

Plate models

Allen et al. (1969, 1970), Gausman et al. (1970), Jacquemoud et al. (1990, 1996, PROSPECT), Fourty et al. (1996), Baret and Fourty (1997)

layers

Discrete objects models

Dawson et al. (1997, LIBERTY), Ganapol et al. (1998, LEAFMOD), Ma et al. (1990)

N-flux models

Allen and Richardson (1968), Andrieu et al. (1988), Fukshansky et al. (1991), Martinez v. Remisowsky et al. (1992), Richter and Fukshansky (1996), Yamada and Fujimura (1991), Conel et al. (1993)

τs = scattering coefficientk = absorption coefficient

Stochastic models

upperepidermis

palisademesophyll

spongymesophyll

lowerepidermis

upperepidermis

palisademesophyll

spongymesophyll

lowerepidermis

absorbed

scattered

illuminationtop

directlyreflected

diffusereflected

illuminationbottom

directlyreflected

diffusereflected

Tucker and Garratt (1977, LFMOD1), Lüdeker and Günther (1990), Maier et al. (1997, SLOP)

Ray tracing models

Govaerts et al. (1996, RAYTRAN), Jacquemoud et al. (1997), Baranoskiand Rokne (1997, 1998, 2000, ABM), Ustin et al. (2001)

λ (μm)

1 0- 1

1 TM 6TM

WATER SCATTERING

1 0- 3

λ (μm)

WATER ABSORPTION

0 2 0 4 0 6 0 8 0 1 0 0 1 2 00

Pure Water

Absorpt ion coefficient of liquid water (1/cm)

0.0000

0.0001

0.0002

0.0003

0.0004

0.0005

0.0006

0.0007

0.0008

0.0009

0.0010

0.0011

0.0012

0.0013

0.0014

400 500 600 700 800 900 1000

wavelength (nm)

PROSPECT-I

PROSPECT-II

LIBERTY

CHLOROPHYLL ABSORPTION

OldNew

400 500 600 700 800 900 1000

1015202530354045505560657075808590

400 600 800 1000 1200 1400 1600 1800 2000 2200 2400 2600

wavelength (nm)

CELLULOSE+LIGNIN ABSORPTION

PROTEIN ABSORPTION

OldNew

500 1000 1500 2000 2500

DRY MATTER ABSORPTION

PROSPECT - Sensitivity analysis

400 600 800 1000 1200 1400 1600 1800 2000 2200 24000

Wavelength (nm)

NCabCwCm

After Jacquemoud et al.

400 450 500 550 600 650

zeaxanthin-violaxanthin

wavelength (nm)

400 450 500 550 600 650

violaxanthinzeaxanthin

wavelength (nm)

Sodankyla, Finland

SIFLEX data

absorption

An absorption spectrum (a) shows a vibrational structure characteristic of the upper state

A fluorescence spectrum (b) shows a structure characteristic of the lower state, displaced to lower energies (mirror image of the absorption)

Chlorophyllfluorescence

spectral emission

Source

Sample

Detector

Effects offluorescence

on vegetationreflectance

2-5 %20-30 %

Turbid Geometric Hybrid Ray Tracing

++++++++(+)+Process time

+++++++++++Accuracy++++++++(+)+Parameters

Ray TracingHybridGeometricTurbidModelsCriteria

Turbid models are the most convenient to invert actual remote sensing data

Ray-tracing models are the most realisting for detailed forward modelling

- Geometric models are not adequate when dealing with multiplescatering (i.e., in the near infrared)

- Ray-tracing models are usually not-invertible (too realisticrequire many input variables)

- The detailed geometric representation of the scene can beused as statistical representation (one case from the manypossible)

- Hibrid models tend to be used in a wrong way (inconsistenttreatment of first-order and multiple-order scattering)

Accounting for varyingillumination conditions(direct versus diffuse light)

Gap FractionP(θ,ϕ)

⎟⎠⎞⎜

⎝⎛ −

⎥⎦⎤

⎢⎣⎡

μΔϕθϕθλ−⎥⎦

⎤⎢⎣⎡

μΔϕθ−=ϕθ

0),(),(1.),(1),(

Markov Gap Fraction ModelAdjustmentλ(θ) and ΔL

⎥⎦⎤

⎢⎣⎡

μϕθ−=ϕθ ),(),(0

LAIGExpP

Poisson Gap Fraction Model ( Turbid RTM)

Comparisonμ=cos(θ)

Solar beam

Vegetation

λ(θ,ϕ)

•λ=1 ‘random structure’

•λ>1 ‘regular structure’

•λ<1 ‘clumped structure’

Canopy Gap Fraction Models

Rochdi and Baret

LAI=0.5

Gap fraction as a function of the viewzenith angle and theleaf-stem translation factor (χ) for smallleaves

400 700 1000 1300 1600 1900 2200 2500

lea f r e f le ct a nce

le af t r ansmi t t a nce

lea f absor pt a nce

so il r ef le ct a nce

wavelength (nm)

400 700 1000 1300 1600 1900 2200 2500

soil directcanopy directmult iple scat teringtotal ref lectance

wavelength (nm)

CHANGES IN LEAF SIZEλ = 675 nm

view angle-90 -80 -70 -60 -50 -40 -30 -20 -10 0 10 20 30 40 50 60 70 80 90

0 .0 2

0 .0 6

0 .0 4

0 .0 8

0 .1 0

0 .1 2

0 .1 4

0 .1 6

0 .1 8

0 .2 0

leaf size values

0.080 .2

Sunλ = 675 nm

CHANGES IN CANOPY HEIGHT canopy height values

view angle-90 -80 -70 -60 -50 -40 -30 -20 -10 0 10 20 30 40 50 60 70 80 90

forward scatteringbackward scattering

MODTRAN 4(650 nm)

maximum

Leaf versuscanopy level

What gives a measurable signal?(LAI x fc) x Cab(LAI x fc) and Cab separately(LAI) and (fc) and Cab separately

All the curves correspondto the sametotal (canopy) Cab !!!

Non photosyntheticelements:spectral variability

SURFACE MODEL PARAMETERISATION:(a) Leaf inputs:

- Leaf effective thickness - Leaf water content- Total leaf chlorophyll (a+b) - Specific leaf weight- Ratio Ca/Cb - Leaf cellulose content- Fraction of Ca in LHCP - Leaf lignin content- Leaf carotenes content

(b) Canopy inputs:- LAI- fCover- Clumping parameter (H/D)

(c) Soil inputs:- Soil wetness parameter

Although there aredifficulties in modellingsome details in thespectral / angularvariability,current modellingcapabilities allowa quite precisereconstruction ofmeausuredspectralreflectance

- Cab = 50.17 μg/cm-2- LAI = 3.73- Cw = 0.0145 g/cm-2- Cm = 0.0036 g/cm-2- N = 1.5

CHRIS/PROBA – SAIL/PROSPECT (14/07/03)

Information retrievalbased on optimised

spectral indices

Visible Atmospherically Resistant Index

Verhoef and Bach, 2007

Retrievals from hyperspectral data:

Canopy watery = 3,1431x + 857,

R2 = 0,5797

-100 0 100 200 300 400 500 600 700 800 900

Corn bar1_12Subarbeet_bar1_12Barley bar1_12Wheat_bar1_12Alfalfa bar_1_12Corn bar2_12Sugarbeet bar2_12Barley bar2_12wheat bar2_12Alfalfa bar2_12Sugarbeet bar1_9Alfalfa bar1_9Sugarbeet bar2_9Alfalfa bar2_9Sugarbeet bar1_15Alfalfa bar1_15Subarbeet bar2_15Alfalfa bar2_15

y = 0,0359x + 0,347R2 = 0,3789

-100 0 100 200 300 400 500 600 700 800 900

Corn bar1_12Sugarbeet bar1_1Barley bar1_12Wheat bar1_12Alfalfa bar1_12Corn bar2_12Sugarbeet bar2_1Barley bar2_12Wheat bar2_12Alfalfa bar2_12Sugarbeet bar1_9Alfalfa bar1_9Sugarbeet bar2_9Alfalfa bar2_9Sugarbeet bar1_1Alfalfa bar1_15Sugarbeet bar2_1Alfalfa bar2_15

Leaf chlorophyllLeaf chlorophyll

MERIS Terrestrial Chlorophyll Index (MTCI)

3 0 0 5 0 0 7 0 0 9 0 0 1 1 0 0 1 3 0 0 1 5 0 0 1 7 0 0 1 9 0 0 2 1 0 0 2 3 0 0 2 5 0 0

L A I= 4

λ (n m)

0 .0 0 1

0 .0 0 2

0 .0 0 4

0 .0 0 6

0 .0 1 0

0 .0 1 5

0 .0 2 0

0 .0 4 0

0 .0 6 0

0 .0 8 0

0 .1 0 0

LeafWat er

Co nt ent (cm )

0 .0 0 0 .0 1 0 .0 2 0 .0 3 0 .0 4 0 .0 5 0 .0 6 0 .0 7 0 .0 8 0 .0 9 0 .1 0

LAI=1LAI=4

leaf liquid water (cm)

0 . 5 0

0 . 5 5

0 . 6 0

0 . 6 5

0 . 7 0

0 . 7 5

0 . 8 0

0 . 8 5

0 . 9 0

0 . 9 5

1 . 0 0

Results for AVIRIS channel 63 (968.2 nm)

0 .0 0 0 .0 1 0 .0 2 0 .0 3 0 .0 4 0 .0 5 0 .0 6 0 .0 7 0 .0 8 0 .0 9 0 .1 00 . 2 5

0 . 3 0

0 . 3 5

0 . 4 0

0 . 4 5

0 . 5 0

0 . 5 5

0 . 6 0

LAI=1LAI=4

leaf liquid water (cm)

Simplified method:modelling of liquid water absorption depth

as direct retrieval by a simple method

as first-guess for more sophisticate algorithms

Information retrievalbased on optimised

model-inversion techniques

• turbid medium• separation green / senescent parts: LAIT = LAIG + LAIS

The problem of model inversion can be considered fromdifferent perspectives:

(a) Root finding of a given function

(b) Solving non-linear set of equations

(c) Function minimisation

(d) Non-linear least-squares modeling of data

Root finding and solving non-linear set of equations wouldrequire that the function is “exact”, and for this reason function minimisation is normally preferred.

Choice of the merit function

Assumptions:

Incorporation of the uncertainties in the inverse process:

[ ] [ ] [ ] [ ]pt

pCRMmest

CRMmes VVCVVVRRWVRR −−+−−= −− 112 )()(χ

The maximum likelihood on the variables minimize:

Residuals

a prioriCovariance Matrix

Residuals

a prioriCovariance Matrix

Radiometric Part Variable Part

Assumptions: Gaussian distribution of the uncertainties

2)(∑ ⎥⎦⎤

⎢⎣⎡ −M

imes VRRσ

∑ ⎥⎦⎤

⎢⎣⎡ −N

ipi VVσif diagonal matrixes

THE SHAPE OF THE MERIT FUNCTION

Absolute minimum at first guess (most probable value)

(location of minimum is variable)

Xmin X max

maximum range of possible values

maximum range of probable values

Xminref Xmax

f (X)non valid solutions

valid solution

absolute minimum

relative minimum

Neuralnetworkmethods

TrainingTheNeuralNetwork

approximations

Simplified model inversion(spectral fitting over restricted spectral ranges)

Spectral-angular synergy:

application of synergy

400 600 800 1000 1200 1400 1600 1800 2000 2200 2400 2600

SUGAR BEET

wavelength (nm)

ALFALFA

Li ne 1 , n oo nLi ne 2 , n oo nLi ne 1 , mo rn in gLi ne 2 , mo rn in gLi ne 1 , a f t e rn oo nLi ne 2 , a f t e rn oo n

SV6 - C03 UTM-X: 577783 UTM-Y: 4324794 LAI = 1.71 fCover = 0.61

Li ne 1 , n oo nLi ne 2 , n oo nLi ne 1 , mo rn in gLi ne 2 , mo rn in gLi ne 1 , a f t e rn oo nLi ne 2 , a f t e rn oo n

V16 - C01 UTM-X: 577550 UTM-Y: 4324069 LAI = 1.84 fCover = 0.95

Homogeneous vegetation:Spectral information dominant

Heterogeneous vegetation:Angular information dominant

RETRIEVAL OF fCOVER(simplified)

RETRIEVAL OF LEAF AREA INDEX (LAI)

- Difficult field measurements (for a given definition)- Variability in ground measurements

- LAI is retrieved linked to some absorber component:* chlorophyll* water* dry matter

- Coupled to fractional cover (view angle dependent)

- Difficult independent validation of LAI(coupled to other variables)

700 900 1100

λ (nm)700 900 1100

λ (nm)

LAI = 1 LAI = 40.6

Line-fittinggives LAI aslinked to theslope of theedge of theabsorption

feature

Unique capability ofhigh spectral

resolution data

Inter-channel radiometric calibrationInstrumental spectral shiftsRadiometric noisesNatural intra-species variability (LAI changes)Natural spectral shifts (substrate bonds)Natural inter-species variability...

ADVANTAGES OF UNIFORMCONTIGUOUS SPECTRAL COVERAGE

- based on liquid waterabsorption properties

- accounting for canopygeometry effects

RETRIEVAL OF LEAF WATER CONTENT

non-linear fitting algorithm over a limited spectral range

line-fitting algorithm(non linear)over the 860 nm - 1320 nmlimited spectral rangeaccounting only forleaf water absorption

Decoupling of atmospheric effectswhen retrieving leaf / canopyinformation

[ 860 , 1320 ] nm

[ 1070 , 1320 ] nm[ 860 , 1080 ] nm

DAISEX-2000HYMAP data

atmosphericover-correction

potentialspectral shift

WATER VAPOURSPATIAL VARIABILITY

- very high spatial resolution watervapour maps (turbulence structure)

Residual atmosphericwater vapour effectson DAISEX-HYMAP data

1 .1 01 .0 51 .0 00 .9 50 .9 00 .8 5

atmospheric water vapour

surface liquid water

wavelength ( m)μ

“depth” is not always the bestindicator to determineamount of absorber by measuringreflectance acrossan absorption band

Influence of pigmentsdistribution within the leaf(for a given total leafchlorophyll content)

- potential separabilityof chlorophyll a and b

RETRIEVAL OF LEAF CHLOROPHYLL CONTENTline-fitting algorithm (non linear) over the 530 nm - 740 nm limitedspectral range accounting only for chlorophyll absorption

High modelling variability !

Are all pigmentsseparable in the signal ?

Key issues:- existing model parameterisationsdo not account for the observedvariability

- high variability set limits to thepossible decomposition of effectsdue to different pigments

[ 530 , 740 ] nm

restricted spectral interval(to improve in cases withvery low chlorophyll content)

optimum spectral interval

ROSIS data

HYMAP data

Retrievals from multi-angular data:Improvements in retrievals of:- LAI- fractional cover

Retrievals ofnew variables:- leaf size (d)- canopy heigh (h)

Compensationof angular effectsin other datasets

Weiss et al., 2001

Couplingcanopyfunctioningand radiativetransfermodels forremote sensing data assimilation

- Succesful results, intensively validated by means ofsimultaneous ground measurements of all relevantsoil / canopy / atmosphere properties

- Difficulties in retrieving biophysical variables whenconstraining models in all (most significant) inputsvariables: the accuracy in the retrieval of someparticular variable should not be compromisedat the expenses of wrong values for other key variables

- Use of multiple views to constraint LAI and fCoverretrievals (coupling of biochemicals andcanopy structure): alternative formulations allow toretrieve LAI = f(view angle) and then use such functionto derive structural properties (perticularly for the caseof suboptimal sampling of surface BRDF)

Advanced retrievaltechniques:

multi-sptep procedures

spectral channels

multi-resolution spatial classification

homogeneity test

convergence test

heterogeneous pixels: mixture model inversion

homogeneous pixels: reflectance model inversion

Nth iteration parameters

a iN{ }

i = 1 , ... , P

unmixing procedure

end-members parametric

characterisation

end-members definition (soil, vegetation, shade...)

preliminary values from empirical relationships

heterogeneous pixel masking

additional outputs

generation of a complete output map for each variable(merge homogeneous + heterogeneous pixel outputs)

A general multi-step procedure

- Explicit separation of almostpure pixels from spectral mixtures

- Use of several retrieval techniquesfor each step

- Produce different adequate outputsfor each retrieval procedure

Such methods are used in practice for

real images

MODIS LAI/FPAR Retrievals: Main and Back-Up Algorithms

Main algorithm: during retrievals, surface reflectances predicted by RT model are compared with MODIS channel data (Red and NIR) and when agree corresponding LAI and FPAR are retrieved. The RT simulations are performed with the Stochastic RT model which accounts for 3D effects of vegetation heterogeneity with pair-correlation function. RT simulations are parameterized with vegetation type, leaf optical properties, soil reflectance patterns. Main algorithm delivers most accurate retrievals, based on best quality input.

Back-Up algorithm: If Main algorithm fails due to input (or RT model) uncertainties, the back-up algorithm retrieves LAI/FPAR from NDVI. Those are low accuracy retrievals, based on low precision input.

Main algorithm Back-Up algorithm

Validation of retrievals

Intensive field measurements

Ground measurements: Mean values

V29 V20 V14B V1

Individu al samples

- vegetation properties- soil properties- solar radiation- atmospheric status- surface fluxes

spatial variability

- Statistical representativity of measurements used for validation

- Strategy for spatial and temporal sampling

- Validation methodology versus retrieval technique

- Statistical extrapolation of results (sample versus population)

- Adaptation of different methodology for each biophysical parameter

- Examination of results in view of the expected limitations

- Adaptability to the application

- Critical review of actual achievements

avg = 3.07; std = 1.45

Many types of crops:alfalfacornsugarbeetonionsgarlicpotato....

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

LAI Alfalfa Corn Sugarbeet

LAI measurements

113 Elementary Sampling Units (24 data samples each ESU)

covering the full LAI range

FRACTIONAL VEGETATION COVER

CROP Chlorophyll mean value per crop (mg*cm-2) FVC mean value per crop

C1 51 0.63 B, B3 44 0.94 On-1 20 0.64 G1 14.5 0.12 P1 35.5 0.96

Mean values per crops

Hemispherical Photographs (+) for LAI and FVC estimation

A9 A1 A10 P1 C2 C1 C3 C G1 B3 B ON1SV Vine GS

FVC_HP_A9FVC_HP_A1FVC_HP_A10FVC_HP_P1

FVC_HP_C2FVC_HP_C1FVC_HP_C3FVC_HP_C

FVC_HP_G1FVC_HP_B3FVC_HP_BFVC_HP_ON1

FVC_HP_SVFVC_HP_VINEFVC_HP_PAFVC_HP_GRASS

Fraction of Vegetation Cover (FVC)

C R O P F IELD S ESU s C orn C 3,C 2,C 1,C 9

A lfa lfa A9,A10,A1 15 Sugarbeet B3,B 6

O nions O N 1 2 G arlic G 1 3 Potato P1 6

Vineyard V 3 Papaver PA 1

G rass G rass 4 Fruit trees 2 4

Sparse Vegetation SV 2 TO TA L 18 55

ESUs description

Sources of problems:

1. image data quality (calibration, noises, pre-processing)

2. ground data quality

3. simplifications in theoretical models

4. adequacy of retrieval methods

All at the same level of importance ?

Scaling issues

Simultaneous NOAA AVHRR / Meteosat data composite (Iberian Peninsula)

Landsat TM data (La Mancha)

AVIRIS data (Barrax)

RESAMPLING OF MULTI-RESOLUTION DATA

- Scaling analysis requires co-registrationof multi-resolution data

- Co-registration of multiple angular viewsrequires to handle multi-resolutionresampling techniques

- BRDF reconstruction with differentpixel size for each view angle requirescompensation of varying GFOV

- Details are specific for each sensor, but a generic procedure is possible

PIXELS GEOMETRY

(36x36 matrix)(1x36 vector)

RESAMPLINGMETHOD

(1x36 vector)

Spatial DegradationOriginalLANDSAT TM data

Optimum Interpolation

NOAA AVHRR dataOriginal

MERIS FR data

CHRIS/PROBA data

SCALINGASPECTS

= 500 mσ

= 250 mσ

= 750 mσ = 1000 mσ

= 100 mσOriginal

NDVI (NDVI)σ(Averaged)

0.0 0.2 0.3 0.40.1

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

NDVI (Averaged)

(NDVI)σ

Scaling issues require the use of statistical techniques (spatialstatistics) to quantify the observed effects beyond thequalitative interpretation of differences

VIS/NIR/SWIR Colour Composite Thermal data

Multiresolution data

1.25 m

3.75 m

12.0 m

Advanced Optical Theory - 2 Retrieval of...

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