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Characterization of Spatial Heterogeneity for Scaling Non Linear Processes

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1. Characterization of Spatial Heterogeneity for Scaling ... S. Garrigues1, D. Allard2, F. Baret1. 1INRA-CSE, Avignon, France. 2INRA-Biom trie, Avignon, France ... – PowerPoint PPT presentation

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Title: Characterization of Spatial Heterogeneity for Scaling Non Linear Processes


1
Characterization of Spatial Heterogeneity for
Scaling Non Linear Processes
S. Garrigues1, D. Allard2, F. Baret1.
1INRA-CSE, Avignon, France 2INRA-Biométrie,
Avignon, France
2
1. Background

Non linear process
Technological constraints Coarse spatial
resolution sensor
Need of high time frequency data
3
2. Problematic
Image spatial structure depends on vegetation
type
20m SPOT NDVI image
4
2. Problematic
Image spatial structure depends on vegetation
type
5
2. Problematic
Image spatial structure depends on sensor spatial
resolution
Homogeneous (Guyana Forest)
Heterogeneous site (Alpilles Cropland )
  • The sensor integrates the signal over the pixel
    intra-pixel variance lost
  • Spatial heterogeneity depends on the spatial
    resolution

6
2. Problematic
Spatial heterogeneity and non linear process
7
2. Problematic
  • Spatial structure (i.e. spatial heterogeneity)
    depends on
  • surface property variation
  • sensor regularization
  • spatial characteristics spatial resolution,
    support geometry (PSF),
  • viewing angle
  • spectral characteristic, atmospheric effects
  • image extent
  • Working scale the field scale
  • Utilisation of high spatial resolution (SPOT 20m)
    to characterize ground spatial structure at field
    spatial frequency.
  • Spatial heterogeneity definition
  • quantitative information characterizing the
    ground spatial structure
  • spatial variance distribution of the variable
    considered, within the coarse resolution pixel
  • Our aim using spatial heterogeneity as an a
    priori information to correct biophysical
    estimation biais, i.e. to scale up the transfer
    function at coarser spatial resolution

8
3. Spatial heterogeneity characterization
Stochastic framework for image exploitation
  • The image is a realization of a random process
    (random function model) with the following
    characteristics
  • Ergodicity one realization of the random process
    allows to infer the statistical properties of
    the random function.
  • Stationarity of the two first moments
  • - the mean image value is constant over the
    image
  • - the correlation between two pixel values
    depends only on the distance between them.
  • Data support SPOT pixel considered as punctual
  • No accounting for SPOT regularization (PSF)
  • No accounting for SPOT pixel radiometric
    uncertainties (measurement errors)
  • Variable studied NDVI

9

3. Spatial heterogeneity characterization
The variogram a structure function
  • Definition
  • spatial variance distribution of the
    regionalized variable z(x)

10

3. Spatial heterogeneity characterization
Spatial structure characterization by the
variogram

11

3. Spatial heterogeneity characterization
Spatial heterogeneity typology



Integral range
Integral range is a yardstick that summarizes
variogram on the image
12
4. Spatial heterogeneity regularization with
decreasing spatial resolution
Spatial structure regularization is a function of
sensor spatial characteristics
Sensor regularization
Puechabon site
13

4. Spatial heterogeneity regularization with
decreasing spatial resolution
Spatial heterogeneity quantification




14
5 Bias correction model
Univariate Model
15

5. Bias correction model
Cropland site (Alpilles) example
Resolution500m



  • Model problem
  • Non stationnarity pixel sample dispersion
    variance (pixel spatial heterogeneity) is lower
    than theoretical variance dispersion predicted by
    variogram model

16

5. Bias correction model
Cropland site (Alpilles) example
Resolution500m



  • Model problem
  • Non stationnarity pixel the sample dispersion
    variance of the pixel is lower than the
    theoretical variance dispersion predicted by the
    variogram model

17

5. Bias correction model
Cropland site (Alpilles) example
Resolution1000m




18
6. Multivariate spatial heterogeneity
characterization
Multivariate description of spatial heterogeneity
Coregionalization variogram model
Alpilles (Cropland)
  • multi-spectral spatial heterogeneity
  • description
  • more information on physical signal
  • using variance-covariance dispersion matrix to
    correct bias
  • Problems disturbing factors (atmosphere)
    influence the spatial structure

19
5. Conclusions and prospects
  • Using variograms to describe spatial
    heterogeneity
  • it describes the spatial structure of different
    landscapes
  • it allows to model data regularization
  • Bias correction model
  • based on variogram models and accounts for the
    non linearity of the transfer function
  • allows accounting for actual PSF (sensor spatial
    characteristics, registration for data fusion)
  • Problems
  • How to adjust variogram models for bias
    correction?
  • Temporal stationnarity of the variogram models?
  • Transfer function diversity development of a
    multivariate model
  • Accounting for image spatial information for
    quantitative remote sensing is an important
    concern
  • Use of SPECTRA data to adjust variogram models
    and investig
  • ate their temporal stationnarity
  • Optimizing the PSF design of future missions

20
Raffy Method Univariate case
21
2. Problematic
Spatial heterogeneity and non linear process
Non linear transfer function between NDVI and LAI
LAIf(NDVI)
LAIB
NDVIB
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