[ieee 2014 third international conference on agro-geoinformatics - beijing, china...

Provincial Spatial Sampling Method for Crop Sown Acreage Estimation

Dong Zhaoxia Key Laboratory of Agri-informatics, Ministry of Agriculture

Institute of Agriculture Resources and Regional Planning, Chinese Academy of Agriculture Sciences

Beijing, China

An Yi The Management Office of Miyun Reservoir

Beijing, China

Wang Di Key Laboratory of Agri-informatics, Ministry of Agriculture


Beijing, China

Zhou Qingbo Key Laboratory of Agri-informatics, Ministry of Agriculture


Beijing, China

Abstract—Timely and accurate estimating crop sown acreage is one of key technologies of crop yield monitoring by remote sensing, it has become an important subject in national agricultural condition monitoring field. In view of the problems occurred in the current sampling survey technology system, such as the formulation of sample size is lack of scientific, the samples are optionally distributed in space, and the accuracy of population extrapolation are still poor. In this study, Remote Sensing, Geographic information systems technology and traditional sampling methods are used to conduct a study on provincial spatial sampling methods for crop sown acreage estimation, in order to improve the existing sampling survey efficiency. Shandong Province, China is chosen as the study area and winter wheat sown area as the study object. The basic geographic information data (1:250000, province and county boundaries), land use data (1:250000) in 2010, the spatial distribution data of winter wheat (derived by MODIS image) in 2010 and the winter wheat planting regionalization data of the study area are used in this paper. Firstly, two-stage sampling method is employed as the main sampling scheme, considering the convenience of sampling frame construction and samples field investigation; Secondly, all counties in Shandong Province are served as the sampling units of the first stage, 4 kinds of sampling methods (simple random sampling, stratified sampling with the winter wheat planting regionalization as stratification sign, stratified sampling with cultivated land types as stratification sign, stratified sampling with winter wheat sown area in each county as stratification sign) are selected to draw the samples of the first stage, and then sampling cost and errors are evaluated to optimize spatial sampling method of the first stage, based on the samples drawn by the 4 sampling methods; Thirdly, 500 m×500 m are selected as the sampling units size, and simple random sampling method is used to draw the samples of the second sampling stage. 8 levels of sampling size are formulated in the second sampling stage to optimize sample size; Finally, the experiment on population extrapolation and error estimation is conducted based on the samples drawn at the first

and second stage. The experimental results demonstrate that the efficiency of the stratified sampling which the winter wheat area in each county was selected as stratification sign is the highest among 4 sampling methods, when the relative errors of population extrapolation are nearly equivalent; The relative errors decrease with the sample size of the second sampling stage increasing, but the coefficient of variation (CV) is still higher. Comprehensively evaluating the relative error and CV of population extrapolation at 8 kinds of sample size levels, 9 samples drawn from the every sampled county are considered as the optimal sample size at the second sampling stage. In this way, this research can provide a theoretical basis for improving the efficiency of spatial sampling survey for crop sown acreage estimation.

Keywords—spatial sampling; crop sown acreage; two-stage sampling; sample size; extrapolation; error analysis

I. INTRODUCTON The sown area, yield and other information of food crop

are the important basis for the country formulating food policy and economy plan [1-5], And the prompt and accurate estimation of sown area of crop is one of the key technologies of remote sensing-based yield estimation, which has become the significant project of remote sensing monitoring of national agricultural condition [6-8]. Because of decentralizing land usage right, broken cropland and complex plantation structure [9] caused by the current land use system of our country and limiting factors like available ability of remote sensing and work load of image post-processing, remote sensing monitoring of crop sown area of large regional scale cannot be complemented without spatial sampling [10-14]. For example, American Large Area Crop Inventory Experiment (LACIE) and Agriculture and Resources Inventory Surveys through Aerospace Remote Sensing (AGRISTARS) employ area sampling frame method to implement crop area sampling estimation [3]. Based on remote sensing image to help layering

It is supported by National Nonprofit Institute Research Grant of CAAS (IARRP-2014-17), financially.

and measure the crop sown area of sampling land, EU Monitoring of Agriculture with Remote Sensing (MARS) employs stratified sampling method to estimate the sown areas of 17 kinds of crops [15-16]. Chinese scholars have related research on using spatial sampling method to estimate crop sown area. For example, Chen [3], Liu [13] and Jiao [17] employ stratified sampling to estimate the sown areas of rice, wheat and other crops on the basis of remote sensing image data and the related basic geographic information data of study area. Wu and Li [9] put forward estimating sown area of crop with the combination of cluster sampling and spline sampling technology on the basis of crop planting structure division.

Aiming at the problems of existing operational spatial sampling technique system of crop sown area in national ministry of agricultural condition remote sensing monitoring of national ministry of agriculture, such as insufficient scientificity to confirm the sample size; over random spatial sampling layout; lacking of population extrapolation and theoretical basis of error estimation, this study, taking Shandong province as the study area, winter wheat as the study object, through the joint application of the “3S” technology and the traditional sampling method, implements spatial sampling experimental investigation of crop sown area with remote sensing sample survey method, aiming at providing reference for improving the current spatial sampling technology of crop area.

II. RESEARCH METHOD

A. Technical route The research idea of special sampling of crop sown area

mainly includes 4 steps:

1) Basic data preparation of sampling.It mainly includes the basic data needed by scheme design of spatial sampling, including basic geographic information data of study area, spatial distribution data of latest cropland and winter wheat of study area;

2) The design of spatial sampling scheme. On the basis of the above sampling basic data, employ two-stage sampling design to implement sample selection, including spatial sampling method optimization of first stage and sample selection of second stage;

3) Sample observation. On the basis of spatial distribution data of winter wheat of study area, employ GIS (geographic information system, GIS) software to acquire observation of selected sample;

4) Population extrapolation and error estimation. On the basis of the observation of selected sample, employ the population extrapolation and error estimation provided by sampling technique of the two stages to complete the population extrapolation the error estimation of winter wheat area of study area.

B. Study area Shandong province is situated between 34°22′54″N and

38°27′00″N and between 114°47′30″E and 122°42′18″E, on the verge of the Bohai Sea and the Yellow Sea and apart from Korean peninsula and Japanese archipelago by sea. The total

land area of the whole province is 157,000 Km2; the offshore sea area is over 170, 000 Km2. The whole province is divided into 17 prefecture-level administrative regions with 139 county-level administrative regions. Shandong province is located in warm temperate zone and semi-humid monsoon region, with moderate climate, concentrated rainfall and four distinctive seasons. The annual mean temperature is from 11�to 14�, the amount of precipitation is from 550 to 590 mm and the frost-free period is more than 200 days. Shandong province is located in Huang-Huai plain and is the main producing area of winter wheat in our country.

C. Data It mainly includes 4 parts: Basic geographic information

data. Administrative boundary data of Shandong province (1:250000, provincial boundary and county boundary); Land use data. 1:250000 land use data of Shandong province in 2010 (1:250000, including 3rd-level land use type); Spatial distribution data of crop. The spatial distribution data of winter wheat of Shandong province in 2010(based on MODIS image, the spatial resolution is 250 m); Regionalization data of winter wheat plantation of Shandong province. Fig. 1 and Fig. 2 are cropland spatial distributions in study area and winter wheat spatial distributions in study area.

Fig. 1. Cropland spatial distributions in study area

Fig. 2. Winter wheat spatial distributions in study area

D. Sampling scheme design 1) Sample investigation unit design:To accurately acquire

the cultivated area of winter wheat of sample and improve sampling population extrapolation accuracy, this study takes

ground quadrat as sample investigation unit.In comprehensive consideration of the workload and operational complexity of sampling fielding investigation and the representative reflection of actual plantation condition of winter wheat from sampling area, select square grid of 500m×500m as the shape and dimension of ground quadrat.

2) Spatial sampling method design:Employ sample investigation unit dimension to subdivide overall study area, forming 613904 overall units of total. If employing single stage sample design, estimation of the sampling frame structuring and overall relevant parameter (mean value, variance, etc) will be more difficult. To ensure the operability of organizing and implementing sample design and sampling fielding investigation, this study designs two-stage sampling method, to structure sampled population by stages. In other words, taking all counties of Shandong province as the first stage sampled population, select first stage sample (county) with optimizing spatial sampling method; select ground quadrat (500m×500m square grid) from the selected sampling counties as second-stage sample.

a) First-stage sampling:Implement sample selection of first stage with simple random sampling and stratified sampling (subdivide stratified sampling in accordance with different stratified marks into 3 sampling methods) for a total of 4 common sampling methods.Through comparing sampling expense and errors of 4 methods, realize the optimization of sampling methods.

Simple random sampling: (1) Sampling frame structuring. Take the counties of Shandong province as the first stage sampling basic units. Because the cultivated area of winter wheat on the islands of Shandong province is small, this study will not involve them into sampling population for convenient research. The number of units in first stage sampling frame is 107 without the islands; (2) Sample size calculation; (3) Sample selection. Employ pseudo-random number method to complete sample selection by numbering all investigated counties of study area.

Stratified sampling: (1) Stratum symbol design. Making full use of sampling basic data of study area, the design of this study uses 3 kinds of stratum symbols to complete stratified sampling: 1. Stratify by winter wheat planting regionalization. On the basis of the data of winter wheat planting regionalization of Shandong province and the design principle of the number of stratum (the number of population units in single stratum shall not be too little, which shall be no less than 2), the design is divided into 5 strata. The stratifying result is shown in Fig. 3; 2. Stratify by cropland type. In comprehensive consideration of the spatial attribution of 4 kinds of cropland types and the proportion in the whole cropland, design 4 strata. The stratifying result is shown in Fig. 4; 3. Stratify by winter wheat area of each county. Calculate winter wheat sown area of each sampling unit of first stage with GIS software and arrange the winter wheat area of each county from small to large order. Take largest winter wheat area as the denominator and let the largest winter wheat area divides the winter wheat area of each county. Finally, a sequence of winter wheat area ranging from 0% to 100% is

formed. On the principle of minimizing the variance in stratum and the number of units in single stratum no less than 2, through several calculations, design 4 strata and the stratum boundary is area ratio of 25% (i.e. area ratio of the winter wheat area of each county and the largest area among counties); (2) Sample size calculation; (3) Sample selection. The sample selection of first stage of each stratum is completed by isometry system.

Fig. 3 Fig. 4

Fig. 3. Stratified graph with winter wheat planting districts as stratum symbol

Fig. 4. Stratified graph with cropland classes as stratum symbol

b) Second-stage sampling:Take the sample of first stage as the second-stage sampling population and employ simple random sampling to select the sample of second-stage (i.e. ground quadrat of 500 m×500 m). In order to simplify the process of population extrapolation and error estimation, design select same number of ground quadrats at each sample county. This study designs sampling size of the second stage with 8 levels, i.e. equivalently select 2~9 sampling lands of the second-stage from each selected sample of the first stage.

E. Sample observations This study belongs to earlier testing stage of spatial

sampling technique system operation for crop sown area, to verify population extrapolation accuracy of this sampling method, on the basis of winter wheat spatial distribution data of this study area in 2010, employ GIS software to figure out the winter wheat sown area of 2nd sample as the sample observation to complete population extrapolation and error estimation.

F. Population extrapolation and error estimation 1) Simple random sampling:Employ simple estimator to

complete population extrapolation and error estimation. We need to calculated the total value of population extrapolation and the unbiased estimation of the total value estimator variance.

2) Stratified two-stage sampling: With stratified two-stage sampling, the estimator of

stratified two-stage sampling by the mean value stY of secondary unit [18] is:

∑∑

∑=

=

= ==L

hhhL

hhh

L

hhhh

ts yWMN

yMNy

1

1

1 （1）

∑=

= L

hhh

hhh

MN

MNW

1

is the stratum weight by the number

of secondary units and

hh

n

i

m

jhij

h mn

yy

h h

∑∑= == 1 1 is the mean

number of the sample of hth stratum. Population extrapolation

stYΛ is estimated by formula (2). The unbiased estimation of

the total value estimator variance is calculated by formula (3).

st

L

hhhst yMNY )(ˆ

1∑

=

= （2）

)()()ˆ( 2

1st

L

hhhst yvMNYv ∑

=

= （3）

∑=

−+−=L

h hh

hhhh

h

hhts mn

sffsn

fWyv1

22212

112 ))1(1()( （4）

In the formula: if the population of the first stage is divided into L strata (L=4 in this study) and h represents the stratum number (h=1,2,……,L, the first-stage number of units of hth stratum is Nh and say there are Mh secondary units in each primary units of hth stratum), the number of secondary units in

population will be ∑=

L

hhhMN

1; hijy is the jth secondary

unit index value of ith primary unit of the hth stratum in sample; hf1 is the first-stage sampling ratio of the hth

stratum; hf2 is second-stage sampling ratio of the hth stratum; nh is the number of first-stage sample units of the hth stratum; mh is the number of second-stage sample units of the hth

stratum; ∑=

=hm

jhijhi yy

1is the sum of the index of secondary

units in the ith primary unit of the hth stratum in the sample; hhihi myy /= is the ith primary unit index of the hth stratum in the sample by the mean number of secondary

units;2

1

21 )(

11 ∑

=

−−

=hn

ihhi

hh yy

ns is variance of the primary

units of the hth stratum in the

sample;2

1 1

22 )(

)1(1 ∑∑

= =

−−

=h hn

i

m

jhihij

hhh yy

mns is the

variance of the secondary units of the same primary unit in the sample.

To figure out the quantitative evaluations of error magnitude and stability of population extrapolation of various sampling methods, this study selects two indexes, relative error (r) and the coefficient of variation of the total value estimator (CV) [19]. Because the purpose of this study is to perform the provincial spatial sampling method optimization for crop sown area, this study take the total area calculated by winter wheat classification result of MODIS image in study area as hypothetical truth value of the total value;

III. RESULT AND ANAYSIS

A. Efficiency comparison of various spatial sampling methods Table.1 provides 4 kinds of sampling methods to get the

needed sample size and relative error of sampling population extrapolation for designed population extrapolation accuracy. It can be seen from the figure that under the confidence coefficient of 95%, the sequence of sample size needed by four sampling methods to get 95% of population extrapolation accuracy from large to small is sample random sampling (the sample size is 87, stratified sampling by winter wheat cultivation regionalization (the sample size is 87)), stratified sampling by cultivated land type (the sample size is 82) and stratified sampling by winter wheat area size of each county (the sample size is 37), and the sampling ratio also conforms to the sequence. It can also be seen from the figure that on the basis of the above mentioned sample size, the relative error of the total value of population extrapolation by selecting first-stage sample with four sampling methods (the total value is figured out on the basis of the overall winter wheat sown area calculated by GIS software) ranges from 3.1%～3.8% with unobvious difference.

TABLE I. RESULTS OF RELATIVE ERROR AND SAMPLE SIZE FROM 4 SAMPLING METHODS

No. Name Size of

population N

Designed relative error

/％

confidence coefficient /％

Sample size Sampling ratio /％

relative error of population extrapolation/

％

1 Simple random sampling 107 5 95 87 81.2 3.2

2 Stratified sampling 1 107 5 95 87 81.2 3.1



It means that under the condition of similar relative error of population extrapolation, among four sampling methods, the sample size and sampling ratio to reach the designed population extrapolation accuracy with stratified stratum by winter wheat area of each county is smallest and the efficiency is highest. The spatial distribution of first-stage sample (county) selected by four sampling methods is shown in Fig. 5.

Fig. 5. Spatial distributions of the samples selected by 4 sampling methods in the study area(a. simple random sampling; b. Sample spatial distribution of the stratified sampling by winter wheat cultivation regionalization. c. Sample spatial distribution of the stratified sampling by cultivated land type. d. The stratified sampling by winter wheat area size of each count)

TABLE II. RESULTS OF POPULATION INFERENCE AND SAMPLING ERROR ESTIMATION AT 8 LEVELS OF SAMPLE SIZE IN SECOND STAGE

No. First-stage sample size

Second-stage

sample size

Total sample

size

Relative value /%

CV /%

1 37 2 74 23.2 15.1

2 37 3 111 18.4 11.3

3 37 4 148 16.4 9.1

4 37 5 185 15.3 7.9

5 37 6 222 14.7 7.3

6 37 7 259 13.5 7.5

7 37 8 296 12.6 6.7

8 37 9 333 9.8 6.0

B. The impact of sample size on error estimation of population extrapolation On the basis of the optimization result of first-stage spatial

sampling method mentioned above (see Table.1), complete first-stage sample selection with the stratified sampling

method by winter wheat area size of each county and Table.2 provided the population extrapolation and error estimation result of Shandong winter wheat under the level of 8 kinds of second-stage sample sizes. It can be seen from the figure that with the increasing of second-stage simple size, the relative error of population extrapolation and CV is decreasing. When the second-stage sample size is 9 (total sample size is 333), the relative error of population extrapolation is 9.8% which is lower than the required operational accuracy; but the corresponding CV is 6.0% which is higher than the required operational accuracy. Fig. 6 provides two-stage stratified sampling spatial distribution of Shandong winter wheat sown area under different levels of second-stage sample size. By the way, Fig. 6 is one sample spatial distribution among 10 samplings.

Fig. 6. Spatial distributions of the samples selected by the two-stage sampling method under different sample size. (a. Select 2 secondary samples unit from a primary sample unit; b. Select 5 secondary samples unit from a primary sample unit;)

IV. CONCLUSION To design a spatial sampling method suitable for crop sown

area in provincial study area, this study, with Shandong province as the study area, winter wheat sown area as research object, through combining the “3S” techniques with the traditional sampling methods, design 4 kinds of spatial sampling methods and 8 kinds of sample sizes to perform the spatial sampling method study for winter wheat sown area in Shandong province. The result shows that:

1) As for the first-stage sampling population with individual administrative county as sampling basic unit, when complete first-stage sample selection with 4 kinds of spatial methods and the errors of population extrapolation are similar, the sample size needed by stratified sampling by winter wheat area size of each county is smallest and the sampling ratio is just 34.6% with highest efficiency. So it is optimally selected as the spatial sampling method of first stage.

2) When select regular grid of 500 m×500 m as second-stage sampling basic unit, among existing 8 kinds of sample size, with the increasing of sample size, the relative error of estimator and truth value of population extrapolation is decreasing, but CV of estimator of total population value is still higher. On the comprehensive consideration of relative error and CV of sampling population extrapolation, select 9 samples from first-stage sample unit with simple random

a b

a b

c d

sampling method as the optimal sample size during second-stage sampling.

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