for a regional 
uld analyze its 
rrelation and 
opulation) as a 
ing, and then 
locations, and 
| variances of 
er to obtain a 
lite imagery to 
ed resolution- 
units. There is 
nd influencing 
RIP(s)/RIV(s) 
stics (such as 
o explore the 
(or subspace). 
dependency 
ately) suit the 
ssical statistic 
ve schemes of 
tial sampling 
tively optimal 
founded under 
pectation and 
| a geographic 
global spatial 
unstationary) 
‘is really very 
on being very 
global spatial 
the spatial 
je population 
(s). Thus the 
'epresented in 
utocorrelation 
ctively, which 
int allocation 
kinson et al., 
t an unknown 
dly estimated 
able in object 
letermined by 
2, 1990; Wang 
chnique is an 
ea of which is 
cal ranges) to 
principles and 
ind algorithms 
al, 2004). 
age of winter 
ig images and 
ial correlation 
n, the spatial 
1ulti-stratified 
model mentioned above and the grid cells (ie., pixels or 
multiplied pixels) as sampling objects of population. The 
sampling results (e.g, the total estimation and mean of 
sample/population) were gridded for different levels of 
administrative report units (such as province, county and 
township) to adaptively report in order to make scientific, 
helpful related decision (Wang et al, 2002; Feng, 2010). 
To estimate the total value, related mean and variance of 
regionalized population space (or its each subarea) and obtain 
adaptive inference, a set of valid Kriging optimizing models and 
algorithms of regionalized spatial sampling (Li et al., 2004; Feng, 
2010) may be employed to predict the locally optimal RIP/RIV 
of spatial locations. There is a basic equation, as shows below: 
2-34 0,6 © 
where 2 is the value required to estimate, Z_ (x) (i=12,-,n ) 
is the RIP/RIV of a random sampling object at location x, of 
subarea Z, , and n is the number of a sample, where A, (x,) is 
the proximate (adjacent) weight at x, and S. (x) 21 to reach 
izl 
a unbiased estimation (namely the expectation of prediction 
error EZ, -Z,]-0 ) We can calculate all the unknown 
RIP/RIV's values in z, using the least-squares method and 
draw out their associated spatial distribution plot through which 
the total value (or mean) of sampling population space is 
obtained by an accumulation approach. By betaking the 
Lagrange multiplier method, the minimum (Kriging) variance is 
able to obtain making use of the previous Kriging optimizing 
technique, which is related to the semivariogram of sampling 
space and distribution of sampling locations, but not to the 
RIP/RIV's values of sample locations, and these are greatly 
merited and significant for the design of spatial sampling and its 
optimization. 
3. DATA AND REGION OF STUDY 
3.4 Region of Study 
The North China Plain, also called Huang-Huai-Hai Plain, 
being the second plain (accounting for about one third of the 
whole plain area) in China, is situated with a range of about 32- 
40°N, 114-121°E. The plain covers an area of more than 
380,000K m?, most of which is less than 50m above sea level, 
and it can, generally, be divided into three type units of the 
piedmont sloping plain, alluvial plain and coastal plain and is 
one of the most main regions for grain production in China. 
From an administrative district perspective, it includes the 
municipalities of Beijing and Tianjin, the provinces of Henan, 
Hebei, and Shandong provinces, merging with the Yangtze delta 
in northern Jiangsu and Anhui provinces, in which there are 
more than 320 counties (Gong, 1985; Huang et al., 1999; Liu et 
al 2009;  http//baike.baidu.com/view/416642.htm). Its 
dominant land-use type is cropland wherein more than 10 kinds 
of crops are grown, such as winter wheat, maize, millet, rice, 
peanut, sugar beets, and cotton. 
International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XXXIX-B8, 2012 
XXII ISPRS Congress, 25 August — 01 September 2012, Melbourne, Australia 
3.2 Data and Processing 
In this study, a scene CBERS-02 (China-Brazil Earth Resources 
Satellite program, the second satellite) CCD (Charge-coupled 
Device) image in spatial resolution of 19.5m, which covered a 
extent (35.07-36.29°N, 114.3-115.82°E) of original 7270 x 6930 
pixels centered at 35.6905°N, 115.068°E on 2005-04-04 was 
obtained from the site (http://www.cresda. com/index.php) of 
China Centre for Resources Satellite Data and Application 
(CRESDA). Its corresponding surface area was located in the 
central part of North China Plain (CNP), which was one of main 
producing areas of winter wheat, and given a geographic 
representativeness of this area, its landscape features could 
appropriately represent the geographic characteristics of the whole 
CNP. After the chosen image was pre-processed (e.g., geometric 
calibration, cloud clearing, atmospheric corrections), it was 
aggregated into a expedient modeling image with a spatial 
resolution of 253.5m (about 250m) as a datum source of the 
following mixed-pixel spectral decomposition. Comparing the 
results of mixed-pixel spectral decomposition using the linear 
decomposition, fuzzy C-means clustering, BP (back 
propagation) neural network and support vector machine 
models, their most optimal model and method had been chosen. 
We selected the MODIS (Moderate Resolution Imaging 
Spectroradiometer) data including the ESWIR 8-day and EVI, 
Red, NIR and Blue 16-day composite Level 3 products from 
2003-10 to 2004-06 over the CNP. Then, they were processed 
using the image-mosaicking, data phase-matching, and second 
order principal component analysis (PCA) (based on 
corresponding-time and multi-temporal data) techniques, 
wherein the spatial resolution of 250m was regarded as a 
baseline resolution, and were consequently incorporated into a 
scene as the available datum source in order to retrieve the 
fraction/percentage (as the spatial sampling RIP/RIV) of crop 
(i.e., winter wheat) planting area in its each pixel by betaking 
the above most optimal model and method of mixed-pixel 
spectral decomposition (See Table 1 and Appendix: Figure 1). 
4. RESULTS AND ANALYSIS 
4.1 Determining Sample Point Size 
In this study, the RIP/RIV (i.e., percentage of winter wheat 
planting area in each pixel) distributing maps were the basic 
operated data in spatial resolution of 250mx250m used to 
determine a sample-point (ie, sample-grain) minimum 
(baseline) scale. According to a series of sample-grain scales 
from 250mx250m to 2500mx2500m (where each scale-step 
difference was 250m), we analyzed the correlation 
characteristics of the NCP with the three local spatial 
autocorrelation statistics of Moran’s I,, Geary’s C, and  Getis 
ord G, (Genearal G: G, X G; ) and then calculated their means, 
respectively. The corresponding increments (first order 
differences, namely differences of two adjacent statistic means) 
of the three means are shown in Figure 2. 
We can find out the two difference sequences of Moran’s I, and 
Getis ord G, monotonously increasing in contrast to that of 
Gearys C, monotonously decreasing, and there are three 
principal turning points nearby at the sample-grain scale of 
750m, which indicate that there was evident variation as to the 
autocorrelation mean characteristics in this study region, and