A fundamental approach of quantitatively describing spatial 
correlation makes use of the global and local spatial 
autocorrelation statistics (Anselin, 1988) that present the spatial 
dependencies of regionalized proximity objects with their 
indicator parameter(s)/variable(s) (RIP(s)/RIV(s)) in geographic 
space, which leads to the corresponding spatial two order 
effects of the RIP(s)/RIV(s). The former measures an overall 
spatial dependency of objects in a geographic space and the 
latter probes into the relational heterogeneous characteristics 
(variations) of geographic objects. Since the RIP/RIV (i.e., 
percentage of winter wheat planting area in each pixel), 
extracted from remote sensing images, of spatial sampling in 
this study was a variable, i.e., function of distances between 
spatial locations, the three statistics of Moran's I, Geary's C 
(Cliff and Ord, 1981) and General G (Getis and Ord,1992) were 
used to serve as available statistics of describing global/local 
spatial autocorrelation of the geographic RIP/RIV. 
Given that variability and direction of stability of spatial 
correlations cannot effectively be explored using global and 
local autocorrelation measures, semivariance function and 
semivariogram, being concemed with a technique of 
exploratory spatial data analysis, are often used to clarify 
spatial heterogeneous properties, and they can obviously show 
spatial structure characters of geographic RIP(s)/RIV(s) (i.e., 
dependencies of which are dominantly described) and are thus 
very important tools of geographic spatial analysis (Zhuang, 
2005; Wang et al, 2005; Ma et al, 2007). Regionalized 
variation function analysis is implemented under the second 
order (pseudo-)stationary hypothesis and/or the (pseudo-) 
intrinsic hypothesis, which easily results in having the 
experimental semivariance function below: 
N(h) 
: 1 2 
y (h= 2 2 Z(x,)- Z(x, 4 h)] (4) 
where Z(x) and z(x+n) are values of variable z(x) at spatial 
locations x, and x,+h , respectively; N(h) is number of pairs 
of locations separated by a vector 4 (also called lag distance). a 
theoretical semivariance y(4) can be fitted using a set of values 
of an experimental semivariance and the relative models such as 
a linear, spherical, exponential and/or Gaussian model and its 
associated semivariogram be obtained, a shape of which 
represents spatial structuring (or correlation properties ) of 
variable z(x). There are three key parameters of sill (C+C,), 
rang (a) (C,) with 7 (h) 
(semivariogram) that is generally a function of lag h. At a large 
separation distance (a) of h, the semivariogram reaches a 
plateau sill and the related values of z(x), separated by more 
than A, are considered spatially independent, i.e., uncorrelated. 
Those are greatly significant for spatial sampling plan 
(including sample size design and sample-point separated 
distance determination, etc.) and its optimization because of 
collecting non-redundant samples being separated with at least 
the range of correlation apart. A C, is connected with the 
and nugget respect to a 
discontinuity behaviour of a semivariogram near the origin. It 
reflects the continuity of z(x), which is related to either 
uncorrelated noise (measurement error) or to spatial structures 
at spatial scales smaller than the pixel size, and therefore, the 
pertinent nugget effects in this study were neglected. 
  
International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XXXIX-B7, 2012 
XXII ISPRS Congress, 25 August — 01 September 2012, Melbourne, Australia 
   
2.2 Spatial Sampling Design Optimization 
There is a general spatial-sampling paradigm for a regional 
space (or subspace) that in the first place we should analyze its 
spatial structure characteristics (ie, the correlation and 
variation of RIP(s)/RIV(s) of a sampling (sub-)population) as a 
priori knowledge/information of spatial sampling, and then 
decide a sample size, allocate sample-point locations, and 
estimate the total values of and means of and variances of 
sample and (sub-) population and so on, in order to obtain a 
optimal sampling solution. 
Using the RIP(s)/RIV(s) of remotely sensed satellite imagery to 
carry out gridded spatial sampling, we considered resolution- 
level based gridding cells as sampling population units. There is 
a basic principle to find out the unstationary of and influencing 
ranges of local spatial procedures for the RIP(s)/RIV(s) 
betaking the local spatial autocorrelation statistics (such as 
Moran's I, « Geary's C, and G, or G; ) so as to explore the 
sample-point sizes (scales) of sampling space (or subspace). 
Hence, this could avoid the local spatial dependency 
(correlation) to a certain extent and (approximately) suit the 
independent principles of sampling objects in classical statistic 
sampling theory, and then offer a series of selective schemes of 
designing a minimum sample-point size of spatial sampling 
plan. Subsequently, we were able to obtain a relatively optimal 
design of sample-point size by comparing them. 
A global spatial autocorrelation measure is often founded under 
the spatial stationary condition, that is, the expectation and 
variance of the RIP(s)/RIV(s) of spatial objects in a geographic 
space are constant. Although the stationary of global spatial 
procedures does not exist in the real world (i.e., unstationary) 
and even more the hypothesis of spatial stationary is really very 
impossible, especially when the data of population being very 
huge (Ord and Getis, 1995; Anselin, 1995), the global spatial 
autocorrelation can  approximatively display the spatial 
distribution of and trend characteristics of a whole population 
space (or subpopulation) with the RIP(s)/RIV(s). Thus the 
regionalized spatial structure characteristics are represented in 
terms of different perspectives of global spatial autocorrelation 
and regionalized spatial variation measures, respectively, which 
present the basis of application for sample-point allocation 
design of spatial sampling. 
It is essential for the Kriging methodology (Atkinson et al., 
19993; Atkinson et al., 1999b; Journel, 1978) that an unknown 
value Z,(x,) of a continuous variable is unbiasedly estimated 
by the known values Z,(x,) (i=1,2,..,n) of a variable in object 
space using linear model, accuracy of which is determined by 
the variogram function of Kriging (Hou and Huang, 1990; Wang 
et al, 1990; Zhuang, 2005). Ordinary Kriging technique is an 
important type of the Kriging technology, a basic idea of which is 
to employ Kriging blocks (that is, values of local ranges) to 
estimate values of a bigger range. So, based on its principles and 
methods, a set of valid Kriging optimizing models and algorithms 
of regionalized spatial sampling is easily built (Li et al., 2004). 
2.3 Adaptive Analysis and Decision Strategy 
In this study, using the RIP/RIV (fraction/percentage of winter 
wheat planting area in each pixel) of remote sensing images and 
analyzing its spatial structure characteristics (spatial correlation 
and variation) as a priori knowledge/information, the spatial 
sampling was performed, depending on the multi-stratified