From local measurements to high spatial
resolution VALERI maps
M. Weiss, F. Baret
D. Allard, S. Garrigues
10/03/2005
NOV-3300-SL-2857
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From local measurements to high spatial VALERI maps
OVERVIEW OF THE VALERI METHODOLOGY
SPOT
Image
Transfer
Function
(TF)
Level 1 Map
LAI, fCover, fAPAR
(High Resolution)
Co-Kriging
HP
LAI2000
GPS
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Map LAI,
fCover, fAPAR
(Medium Resolution)
Block
Kriging
Level 2 Map
LAI, fCover, fAPAR
+ Flag
(High Resolution)
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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 pixels
Comparing 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 pattern
4 – 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-hull
Transfer function used as an extrapolator
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From local measurements to high spatial VALERI maps
Evaluation of the spatial sampling (5)
2 bands
3 bands
4 bands
TURCO 2003
Red = interpolation
Dark & light blue = strict & large convex-hull
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From local measurements to high spatial VALERI maps
Determination of the transfer function (1)
 Preliminary analysis of the data
Larose, 2003
Haouz, 2003
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Robust
regression
/LUT
Averaging
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Robust
Regression
/LUT 9
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:
k
k 2
Ci
j
1

NbBands
NbBands

k 1

  
j
 i

ik

 


 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
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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)
n
LAI * ( xo )    LAI ( x )   LAI reg ( xo )
 1

LAIreg = LAI issued from transfer function
LAI(x) = LAI measured at ESU 
Minimisation of the estimation variance: s2f(gLAI, LAI , gLAI, LAIreg , gLAIreg, LAIreg ) )
S   = 1
 g(LAI ,LAI )
g(LAI ,LAI reg )   3.73 3.53 
1.17 1.28 
 g(LAI reg,LAI ) g(LAI reg,LAI reg )  3.53 3.38  (1- S1)  1.28 1.93  (1- S2)




 
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From local measurements to high spatial VALERI maps
Collocated kriging (2)
Romilly 2000
 Ordinary Kriging
Few measurements
No actual spatialisation
 Collocated Kriging
High influence of HR image
Require 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
Level
Level
Level
0 : averaging the ESU values
1 : provide HR LAI maps from transfer function
2 : provide HR LAI maps from collocated kriging
0.5: LAI maps derived from SPOT image classification
Year 2000 & 2003 completed
Years 2001 & 2002 partially completed
Year 2004 not investigated
 For some very homogeneous sites, only level 0.5
Aek Loba 2001
Counami 2001,2002
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From local measurements to high spatial VALERI maps
Many thanks for all your contributions
&
May the
10/03/2005
force be with you
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