Title: Characterization of Spatial Heterogeneity for Scaling Non Linear Processes
1Characterization of Spatial Heterogeneity for
Scaling Non Linear Processes
S. Garrigues1, D. Allard2, F. Baret1.
1INRA-CSE, Avignon, France 2INRA-Biométrie,
Avignon, France
21. Background
Non linear process
Technological constraints Coarse spatial
resolution sensor
Need of high time frequency data
32. Problematic
Image spatial structure depends on vegetation
type
20m SPOT NDVI image
42. Problematic
Image spatial structure depends on vegetation
type
52. 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
62. Problematic
Spatial heterogeneity and non linear process
72. 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
83. 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
124. 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
145 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
186. 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
195. 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
20Raffy Method Univariate case
212. Problematic
Spatial heterogeneity and non linear process
Non linear transfer function between NDVI and LAI
LAIf(NDVI)
LAIB
NDVIB