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, -YÀ,G0Z, 6) 5)
where 2. is the value required to estimate, Z, (x;) (i=12:.7)
is the RIP/RIV of a random sampling object at location x, of
subarea Z_ , and n is the number of a sample, where 4. (x,) is
the proximate (adjacent) weight at x, and $4, (;) -1 to reach
i=l
a unbiased estimation (namely the expectation of prediction
error E[Z, -2,]-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
3.1 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
380,000Km?, 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-B7, 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, EX, 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
