Statistics and geographical information system (GIS) are receiving more and
more attention in environmental geochemistry. However, it is important to
know the functions and limitations, the advantages and disadvantages of the
se techniques for better understanding of their applications. Univariate st
atistics is useful for mean calculation, identification of probability dist
ribution and outlier detection. Multivariate analysis plays an important ro
le in the study of relationships among variables. However, while dealing wi
th regionalized variables in environmental geochemistry, the conventional s
tatistics show their shortcomings as they are based on some kind of assumpt
ions for random variables. Spatial analysis makes use of the spatial coordi
nate information of the variables, and also takes the spatial correlation i
nto consideration. However, these pure mathematical methods are still unsat
isfactory as the nature of environmental geochemistry is far from being so
simple. GIS provides visualization and some spatial analysis functions with
much spatial information involved. An expert system is useful for classifi
cation and prediction based on various types of information. However, the r
ule base for expert systems in environmental geochemistry is too small, and
needs to be developed. Problems and possible solutions with the applicatio
n of statistics and GIS in environmental geochemistry are discussed. Exampl
es are based on the authors' experiences in the Yangtze River basin, China,
and in southeastern Sweden. Several ideas are discussed in this paper. A '
robust-symmetric mean' proposed by the authors is one of the best methods f
or mean calculation. For the probability distribution of trace elements, th
e widely accepted 'log-normal distribution' is only a special case of 'posi
tively skewed distributions' which is more adequate. The combination of uni
variate methods and PCA is used to detect outlying samples. Partial least s
quare (PLS) regression, principal component analysis (PCA), cluster analysi
s, discriminant analysis and expert systems may be used to differentiate an
thropogenic anomalies from the natural background. Spatial correlations amo
ng environmental geochemical variables are revealed by cross-variograms. An
environmental information system, with the integration of statistics, GIS,
expert systems and environmental models should be established to further t
he study in environmental geochemistry, as well as to provide decision supp
ort. (C) 1998 Elsevier Science B.V. All rights reserved.