Geography Reference
In-Depth Information
If function values are known on non-uniform grid, then available methods
are nearest neighbor interpolation, natural neighbor, inverse distance
weighting, kriging (one of the geostatistical techniques), and radial basis
function (e.g., Gotway et al., 1996; Robinson and Metternicht, 2006; Namgial
and Jha, 2009). Past studies dealing with GIS applications in water quality
have mostly used geostatistical modeling and inverse distance weighting
techniques for spatial interpolation. It is also revealed from the literature that
geostatistical modeling tool was originally developed to deal with subsurface
studies, and is widely-used for hydrogeologic studies.
5.2.1. Overview of Geostatistical Modeling Technique
Geostatistical modelling is a set of statistical estimation techniques
involving quantities which vary in space (i.e., spatial variables). Geostatistical
techniques for describing and interpolating spatially correlated data take
advantage of the general observation that, on average, values closer together in
space will be more similar than those farther from each other. The steps in
applying these techniques include developing ‗theoretical semi-variogram
models' that describe the spatial variation between pairs of spatially or
temporally related samples and then using these models to estimate sample
parameters and their error variances at unknown locations. Although
geostatistical modelling techniques were originally used in geological sciences
(Journel and Huijbregts, 1978), they have also been frequently applied in
hydrological, agricultural and ecological sciences to evaluate spatial
dependence of surface/subsurface properties and ecological communities, or to
interpolate these parameters (e.g., Goovaerts, 1999; Castrignanò et al., 2000;
Mouser et al., 2005; Schaefer and Mayor, 2007). The process of applying GIS
and geostatistical modelling techniques for developing a spatial distribution
map of a water quality variable is illustrated in Figure 3.
(A) Spatial Estimation by Kriging Technique
In geostatistics, if Z(x) represents any random function for concentration
of any water quality variable measured at n locations in space z(x i ), i = 1, 2, …
n and if the water quality of the function Z has to be estimated at the point x 0 ,
which has not been measured, the kriging estimate is defined as (Journel and
Hujibregts, 1978; Kitanidis, 1997):
n
1
 
 
*
Z
x
z
x
0
i
i
(3)
i
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