10/03/2005 NOV-3300-SL-2857 1

M. Weiss, F. BaretD. Allard, S. Garrigues

From local measurements to high spatial resolution VALERI maps

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From local measurements to high spatial VALERI maps

OVERVIEW OF THE VALERI METHODOLOGY

HPLAI2000GPS

SPOT Image

Level 2 Map LAI, fCover, fAPAR

+ Flag(High Resolution)

Co-Kriging

Map LAI, fCover, fAPAR

(Medium Resolution)

BlockKriging

Level 1 Map LAI, fCover, fAPAR(High Resolution)

Transfer Function

(TF)

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From local measurements to high spatial VALERI maps

Spatial sampling of the Measurements

Objectives = set the minimum number of ESUs at the optimal

location to provide robust relationships between LAI and high resolution spatial images

Get a good description of the geostatistics over the site

In practice = Sample in proportion all cover types & variability

inside Spread spatially equal within 1km² for variogram

computation Not too close to a landscape boundary Sometimes difficulty to access the fields Manpower must be reasonable =3 to 5 ESU per

1km²( 0.18% of the site)=> Need to evaluate the sampling afterwards

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From local measurements to high spatial VALERI maps

Evaluation of the spatial sampling (1)

30 to 50 ESUs to compare with 22500 SPOT pixelsComparing directly the two NDVI histograms is not statistically

consistent

Monte-Carlo procedure to compare the actual cumulative ESU NDVI frequency with randomly shifted sampling pattern

1 – Computing the NDVI cumulative frequency of the 50 exact ESU location 2 – Applying a unique random translation to the sampling pattern

3 – Computing the NDVI cumulative frequency of the shifted pattern4 – Repeating steps 2 and 3, 199 times with 199 random translation

vectors

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From local measurements to high spatial VALERI maps

Evaluation of the spatial sampling (2)

Statistical test on the population of 199+1 cumulative frequencies

For a given NDVI level, if the actual ESU density function is between the 5 highest and 5 lowest frequency value, the hypothesis that ESUs and whole site NDVI distributions are equivalent.

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From local measurements to high spatial VALERI maps

Evaluation of the spatial sampling (3)

SPOT image classification & comparison of SPOT/ESU distributions

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From local measurements to high spatial VALERI maps

Evaluation of the spatial sampling (4)

The convex-hull criterium Strict convex-hull summits = ESU reflectance values in each band Large convex-hull summits = ESU reflectance values in each band ±

5%relative

Pixels inside the convex-hull: transfer function used as an interpolator

Pixels outside the convex-hullTransfer function used as an extrapolator

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From local measurements to high spatial VALERI maps

Evaluation of the spatial sampling (5)

TURCO 2003

Red = interpolationDark & light blue = strict & large convex-hull

2 bands 3 bands 4 bands

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From local measurements to high spatial VALERI maps

Determination of the transfer function (1)

Preliminary analysis of the data

Haouz, 2003 Larose, 2003

Averaging Robust Regression

/LUT

Robust regression

/LUT

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From local measurements to high spatial VALERI maps

Determination of the transfer function

Test of 2 methods Use of robust regression

iteratively re-weighted least squares algorithm (weights computed at each iteration by applying bisquare function to the residuals).

Results less sensitive to outliers than ordinary least squares regression.

Use of LUT composed of the ESU values LUT with nbESU elements (3,4 reflectances + measured LAI) Cost Function:

Estimated LAI = Average value over x data minimizing the cost function

Choice of the best band combination by taking into account 3 errors:

Weighted RMSE RMSE Cross-validation RMSE

NbBands

kki

kj

kij

i NbBandsC

1

21

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From local measurements to high spatial VALERI maps

Determination of the transfer function

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From local measurements to high spatial VALERI maps

Collocated kriging (1)

)( )( )(1

*oreg

n

o xLAIxLAIxLAI

Minimisation of the estimation variance: f(LAI, LAI , LAI, LAIreg , LAIreg,

LAIreg ) )= 1

LAIreg = LAI issued from transfer functionLAI(x) = LAI measured at ESU

)S - (1 .931 28.1.281 17.1 ) - (1 38.3 53.3

53.3 73.3),( ),(

),( ),( 21

SLAILAILAILAI

LAILAILAILAIregregregreg

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From local measurements to high spatial VALERI maps

Collocated kriging (2)

Rom

illy 2

00

0

Ordinary KrigingFew measurementsNo actual spatialisation

Collocated KrigingHigh influence of HR imageRequire linear LAI-Highly decreases the estimation variance

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From local measurements to high spatial VALERI maps

Conclusions: data base status

The spatial sampling & associated methodology are quite well established

Level 0 : averaging the ESU values Level 1 : provide HR LAI maps from transfer function Level 2 : provide HR LAI maps from collocated kriging Level 0.5: LAI maps derived from SPOT image

classification

For some very homogeneous sites, only level 0.5

Aek Loba 2001Counami 2001,2002

Year 2000 & 2003 completedYears 2001 & 2002 partially completedYear 2004 not investigated

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From local measurements to high spatial VALERI maps

Many thanks for all your contributions

&

May the force be with you