STOCHASTIC IMAGING OF ENVIRONMENTAL
DATA
Jean-Jacques ROYER a , and Arben SHTUKAa,b,l
aCNRS Centre de Recherches Pitrographiques et Geochimiques, B.P. 20,
54501 Vandoeuvre-Les-Nancy Cedex, France
bLIAD - ENSG, B.P. 40, Rue du Doyen Marcel Roubault, 54501 VandoeuvreLes-Nancy, France.
ABSTRACT
Interpretation of environmental data is currently confronted with the problem of
estimating the spatial variation of a parameter from a limited number of sample
points irregularly distributed in space. The challenge is to extract the relevant
information for a given problem from the individual observations at control
points. For example, in risk analysis (water resource monitoring, overflow
forecasting, pollution monitoring), the emphasis is on detecting the maximum
value or the anomalies of the appropriate parameter.
Within this framework, classical numerical mapping techniques such as spline
interpolation, multivariate regression or kriging, are of little use, because they
provide an estimation of the mean local value while the expected distribution of
the parameter would be more relevant.
In this paper, a stochastic simulation technique based on indicator functions is
presented. It provides at each unknown point an estimation of the conditional
probability function which can be further used to produce a "Stochastic image" or
a realistic simulation map of the unknown parameter. This technique is also used
to build various non-parametric estimators of an expected value (such as minimum, maximum, median, inter quartile range) which can be used in risk analysis.
A case study in environmental monitoring is presented to illustrate the procedure.
Traitement d'images par Methodes Stochastiques des Donnees
Environnementales
RESUME
L'interpretation des donnees environnementales se trouve confrontee habituellement au probleme de l'estimation de la variation spatiale d'un parametre it
partir d'un nombre limite de points d'ichantillonnage irregulierement distribues
dans l'espace. La difficulte est alors d'extraire des informations pertinentes compte
tenu du probleme pose it partir des observations elementaires effectuees sur des
points de contrOie.
1 To whom correspondence may be addressed
C. Bardinet et al. (eds.), Geosciences and Water Resources: Environmental Data Modeling
© Springer-Verlag Berlin Heidelberg 1997
DATA
Jean-Jacques ROYER a , and Arben SHTUKAa,b,l
aCNRS Centre de Recherches Pitrographiques et Geochimiques, B.P. 20,
54501 Vandoeuvre-Les-Nancy Cedex, France
bLIAD - ENSG, B.P. 40, Rue du Doyen Marcel Roubault, 54501 VandoeuvreLes-Nancy, France.
ABSTRACT
Interpretation of environmental data is currently confronted with the problem of
estimating the spatial variation of a parameter from a limited number of sample
points irregularly distributed in space. The challenge is to extract the relevant
information for a given problem from the individual observations at control
points. For example, in risk analysis (water resource monitoring, overflow
forecasting, pollution monitoring), the emphasis is on detecting the maximum
value or the anomalies of the appropriate parameter.
Within this framework, classical numerical mapping techniques such as spline
interpolation, multivariate regression or kriging, are of little use, because they
provide an estimation of the mean local value while the expected distribution of
the parameter would be more relevant.
In this paper, a stochastic simulation technique based on indicator functions is
presented. It provides at each unknown point an estimation of the conditional
probability function which can be further used to produce a "Stochastic image" or
a realistic simulation map of the unknown parameter. This technique is also used
to build various non-parametric estimators of an expected value (such as minimum, maximum, median, inter quartile range) which can be used in risk analysis.
A case study in environmental monitoring is presented to illustrate the procedure.
Traitement d'images par Methodes Stochastiques des Donnees
Environnementales
RESUME
L'interpretation des donnees environnementales se trouve confrontee habituellement au probleme de l'estimation de la variation spatiale d'un parametre it
partir d'un nombre limite de points d'ichantillonnage irregulierement distribues
dans l'espace. La difficulte est alors d'extraire des informations pertinentes compte
tenu du probleme pose it partir des observations elementaires effectuees sur des
points de contrOie.
1 To whom correspondence may be addressed
C. Bardinet et al. (eds.), Geosciences and Water Resources: Environmental Data Modeling
© Springer-Verlag Berlin Heidelberg 1997