Evaluation on Extrapolation Efficiency of Multiple Estimators for Winter Wheat Planting 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

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

Beijing, China

Chen Zhongxin Key Laboratory of Agri-informatics, Ministry of Agriculture

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

Beijing, China

Abstract—In view of the problem occurred in those studies on crop planting acreage estimation using estimators at home and abroad, such as just one single estimator (simple estimator or regression estimator) is used to extrapolate the population values and estimate sampling errors; the efficiencies of population extrapolation are not evaluated among multiple estimators quantitatively; furthermore, the estimator for crop planting area estimation is not optimized, it limited the improvement of the efficiency of sampling survey consequently. In this study, “3S” technology (Remote sensing, Geographic Information Systems and Global Positioning Systems) and traditional sampling methods are used to conduct a research on evaluating the extrapolation efficiencies of multiple estimators for crop planting acreage. Mengcheng County in Anhui Province, China is selected as the study area and winter wheat planting acreage as the study object. Firstly, 500m×500m is chosen as the sampling unit size and the physical boundaries of cultivated land plots as the sampling unit boundary to facilitate field investigation of the samples. Secondly, the study area is subdivide by the sampling unit with the size of 500m×500m, and the sampling frame is constructed based on the spatial distribution data of winter wheat in 2009 (derived by ALOS AVNIR-2, the spatial resolution is 10m) )and the basic geographic information(1:250000, county boundary). Thirdly, the simple random sampling method is used to draw the samples, and the winter wheat planting acreage in the samples are measured by field investigation and remote sensing image. Fourthly, 3 kinds of estimators (they are simple estimator, ratio estimator and regression estimator, respectively) are constructed by combining the data of winter wheat planting acreage surveyed by remote sensing and the field investigation data of the sampled units, then 3 estimators are used to extrapolate population values and estimate the sampling errors, respectively; Finally, the relative error and coefficient of variation (CV) are selected as the index to quantitatively evaluate the extrapolation efficiencies of every estimator, and the experiment on optimizing the estimator for winter wheat acreage estimation is conducted. The experimental results demonstrate

that, the ground survey accuracy of winter wheat planting acreage in the samples is higher than that of remote sensing investigation, but there are no significant differences between the two survey results; There is a significant direct proportional relationship between the ground survey results of winter wheat planting acreage in all samples and those of remote sensing investigation; The extrapolation efficiency of ratio estimator is the highest (relative error and CV are the minimum, they are 11.01% and 6.20%, respectively), the second is that of regression estimator, and the extrapolation efficiency of simple estimator is the lowest in 3 kinds of estimators. Therefore, the ratio estimator has certain effect on improving the estimation accuracy of winter wheat planting area by remote sensing. In this way, this research can provide a solution for improving the extrapolation efficiency of crop planting acreage at the regional scale.

Keywords—estimator; winter; wheat; planting area; extrapolation efficiency; error analysis

I. INTRODUCTION Crop sown area information is an important basis for the

development of national food policy and economic plans [1-2]. Timely and accurately estimating crop sown area is significant to strengthen crop production management and ensure our food security [3-4]. Previous domestic and foreign large regional scale sampling survey of crop acreage is mostly by building a simple or regression estimator to infer and estimate overall related indexes (such as the overall value, variance, etc) [5-12]. Simple estimator can be constructed simply with linear unbiased, so it is widely used in the early crop sown area sampling surveys [13]. However, its extrapolation of sampling in the overall process is limited to the use of index of survey variable for population estimation and fails to use the auxiliary variable information to further improve the overall extrapolation accuracy, leading to effective deviation. With the rapid development of remote sensing (RS),

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

Geographical Information System (GIS) and other spatial information technologies, constructing regression estimator and the ratio estimator with auxiliary variable information acquired by remote sensing data is gradually applied to people in spatial sampling survey for crop sown area. For example, the American National Agricultural Statistics Service (NASS),taking the data of June Area Survey as sample ground survey data (i.e survey variable), crop spatial distribution information acquired by monitoring and classifying remote sensing images (mainly IRS-AWIFS and LandSat5-TM) as auxiliary variables, builds regression estimator for the all crop area estimation of US. Practice shows that the overall accuracy of American major crops (wheat, corn and cotton) sown area extrapolated by regression estimator is more than 95% [14]. EU Monitoring of Agriculture with Remote Sensing program (MARS) also employs remote sensing data (Landsat-TM or SPOT-XS) to extract the spatial distribution information of EU crops as auxiliary variables. Construct regression estimator with the ground survey data of crop sown area within Segments selected jointly to estimate 17 kinds of the EU crop sown area. The result shows that the relative efficiency of using the regression estimator to estimate major crop area (the ratio of overall estimation variance caused by all sample ground survey using data and the estimation variance caused by regression estimator) is more than 2 [15]. Gonzalez [16] and other people use remote sensing data(Landsat-TM) and the sampling ground survey data of the same year and the previous year to extract crop spatial distribution information as auxiliary variable and construct regression estimator with the ground survey data and auxiliary variable to estimate barley sown area of northeastern Spain. The result shows that when the inter-annual land use of study area status is not changed greatly, use remote sensing images of last year as auxiliary variable for barley area estimation, which can reach a high estimation accuracy. Zhang [17] and other people use Landsat-TM images to get auxiliary variable information, by building ratio estimator to analyzing impact factors on stratified sampling efficiency of winter wheat area.

In summary, for the research on using statistical estimator to complete crop sown area sampling extrapolation population, single type of estimator (such as simple estimator or regression estimator) is mainly used for regional crop sown area estimation , lacking of quantitative comparison on extrapolation population efficiency of crop sown area completed by multiple estimators, failing to implement optimization selection, which prevent further improving efficiency of sample investigation for crops sown area. In view of this, Mengcheng County is selected as study area in Anhui Province, winter wheat sown area as the study object. Construct multiple statistical estimators with winter wheat sown area data acquired by remote sensing and sampling ground survey data. quantitatively compare the population extrapolation efficiency of multiple estimators with relative error and stability of sampling extrapolation population as index to realize statistical estimator optimization selection and provide a solution for further improving the sampling investigation efficiency of existing crop sown area.

II. RESEARCH METHODS

A. Study area Mengcheng County is located in the Northwest of Anhui

Province, the middle of the Huaibei plain. Its administrative region is situated between 32°55'29″N and 32°29'64″N and between 116°15'43″E and 116°49'25″E. The county be shaped like a rectangle with 40 km from east to west and 60 km from north to south. The area is about 2091 km2, including arable land of 1.53×105 hm2. Mengcheng, typical plain region, belongs to semi-humid continental climate in the warm temperate zone. The average temperature of the county was 14.70C the duration of mean sunshine is 2320 hours, the period of average frost-free is 216 days and the average rainfall of many years is 822 mm. With advantageous natural conditions and fertile soil, Mengcheng teems with wheat, rice, corn and other food crops, of which winter wheat is the most important food crop of Mengcheng and its sown area accounts for 70% of arable land.

B. Data It mainly includes 3 parts: 1) basic geographic information

data. The administrative boundary data of Mengcheng County (the scale is 1:250,000, vector format); 2) the spatial distribution data of the winter wheat area. Vector data of the spatial distribution data of the winter wheat area in Mengcheng County in 2009 (based on ALOS AVNIR-2 image; image track number: 162652930; acquisition date: February 12, 2009; spatial resolution: 10 m); 3) the ground investigated sample data of winter wheat sown area (vector format). The ground investigated sample data of winter wheat sown area in Mengcheng County contains 12 samples. In order to perform population extrapolation and error estimates based on the observations, the ground investigated sample data of winter wheat sown area in this study is selected by using simple random sampling method. To ensure the operability of the sampling ground survey, select natural land boundary as the sample boundary. With standard sampling basic unit size of 500 m × 500 m, we divide sampling unit of the study area with natural land boundary as the sample boundary. To be sure, when dividing sampling unit by natural boundary, if the sample unit size exceeds standard design (this study is designed as 20%), area-weighted calculation is required by using the sampling unit for population extrapolation of winter wheat. Winter wheat area was measured by using handheld differential GPS (accuracy: 1.0m~5.0m) in May 10, 2009. In order to reduce measuring error, we measure winter wheat area in each sample for 3 times and then take average value as measured value. It should be noted that the area measured are only the area of winter wheat and excludes the ridge area. Fig. 1 shows the spatial distribution of winter wheat and ground investigated sample. Fig. 2 gives the composition of natural land in ground survey sample (take ground survey sample of No. 5 as example).

C. Bulid estimators 1) Simple estimator:Since simple random sampling

method is used for sample selection, for simple random

sampling, sample mean can be used as population mean, i.e. the simple estimator of population mean is:

∑=

=n

iiy

ny

1

1 (1)

In the formula: y is the sample mean and the simple estimator of population mean Y ; n is the sample size; yi is the winter wheat area of the ith sample, which can be got through ground survey.

Simple estimator of overall value is calculated by formula (2). Unbiased estimator of simple estimator variance of the overall value is calculated by formula (3) [18].

∑=

==n

iiy

nNNY

1yˆ (2)

( ) ( ) ( ) 22

2 1ˆ sn

fNyNY −== υυ (3)

In the formula: Y is the simple estimator of the overall

value; N is the total capacity; ( )Yυ is the simple estimator variance of the overall value; f is sampling ratio ;s2 is the sample variance.

Fig. 1. Spatial distribution of winter wheat in Mengcheng County and ground survey sample

Fig. 2. The component of natural block in ground sample

2) Ratio estimator:To build the ratio estimator, this study put the overall area of winter wheat by ground survey research as target variable Y, the overall area of winter wheat based on remote sensing as auxiliary variable X. The ratio estimator of population mean and total value of winter wheat area in the study area see formula (4) and (5) respectively [19].

XxyXR == ˆyR (4)

Xx

yX

xyY n

ii

n

ii

R

∑

∑

=

===

1

1ˆ (5)

In the formula: Ry is the ratio estimator of the population

mean of winter wheat areas in the study area; RY is the ratio

estimator of total value; R is ratio estimation of population; y is the total sown area of winter wheat area within the sample area based on ground survey; x is the total sown area within the sample area based on remote sensing; y is the sample mean based on ground survey; x is the sample mean based on remote sensing; X is the total value of winter wheat area within the study area based on remote sensing, which can be got by using ArcGIS to acquire the spatial distribution data of winter wheat in 2009,by;yi is the observation of the ith ground sample; xi is the observation of the ith remote sensing investigated sample, which can be got by adding the spatial distribution data of winter wheat and the sample boundary of ground survey.

The ratio estimator variance of the total value is calculated by formula (6) to (10).

( ) ( ) ( )yxxyR sRsRsn

fNY ˆ2ˆ1ˆ 222

−+−≈υ (6)

( )2

1

2

11 ∑

=

−−

=n

iiy yy

ns

(7)

( )2

1

2

11 ∑

=

−−

=n

iix xx

ns

(8)

( )( )xxyyn

s i

n

iixy −−

−= ∑

=111 (9)

∑∑==

i

i

xy

xyR (10)

In the formula: ( )RYυ is the ratio estimator variance of the total value of winter wheat area in the study area; N is the

total capacity; n is the sample size; f is sampling ratio;2

ysis

the sample variance of ground survey;2xs is the sample

variance of remote sensing survey; syx is the covariance of ground investigated sample and remote sensing investigated

sample; R is the overall ratio estimation, Remaining symbols is same as before.

3) Regression estimator:With reference to the construction of the ratio estimator, with winter wheat area acquired by ground survey in study area as target variable Y, winter wheat area acquired by remote sensing survey in study area as auxiliary variable X, build the regression estimator. For simple random sampling, population mean of winter wheat area and regression estimator of total value can be calculated by formula (11) and (12) respectively [19].

( )Xxbyylr −−= (11)

lrlr yNY =ˆ (12)

Fig. 1 Fig. 2

( )( )

( )2

1

12

∑

∑

=

=

−

−−==

n

ii

n

iii

x

yx

xx

xxyy

ss

b (13)

In the formula: lry is the regression estimator of the population mean of winter wheat area in the study area; y is the sample mean based on ground survey; b is a regression coefficient based on sample and can be estimated by sample; x is the sample mean based on remote sensing; X is the population mean of winter wheat area in the study area based on remote sensing; lrY is the regression estimator of the total population value of winter wheat area in the study area; the definitions of remaining symbols are same as that in ratio estimation.

The formula (14) are used to calculate regression estimator variance of total population value[19].

( ) ( )lrlr yNY υυ 2ˆ = (14)

( ) ( ) ( ) ( )[ ]2

121 ∑

=

−−−−

−=n

iiilr xxbyy

nnfyυ (15)

In the formula: ( )lrYυ is the regression estimator variance of total population value of winter wheat area in the study area; ( )lryυ is the regression estimator variance of population mean of winter wheat area in the study area; f is sampling ratio; Remaining symbols are same as before.

4) Calculation of relative error and coefficient of variation:For evaluating quantitatively extrapolation population error and stability of winter wheat sown area based on 3 kinds of estimators, this study selects 2 indexes, the relative error (r) and coefficient of variation (CV) of total population value estimator. CV is used to evaluate the stability of Sampling and Scaling Scheme,The formula (16) are used to calculate the relative error (r) of Sampling and Scaling Scheme, the calculation of CV sees formula (17).

%100ˆ

×−

=Y

YYr (16)

%100ˆ)ˆ(

)ˆ( ×=Y

YvYCV (17)

In the formula: Y is the true value of total population value, based on the winter wheat area by using the regional statistics module in GIS; )ˆ(YCV is the variation coefficient of total population value estimator.

D. Sample observation To build a variety of estimators, this study uses 2 ways to

get the sample observations: one is ground survey. Manual measurement is used to measure winter wheat acreage by

using differential GPS. Another is remote sensing. We can get the sample observations by superposing the spatial distribution data of winter wheat area in the study area (remote sensing image interpretation) and sample survey data (vector format), using GIS to acquire sample observation with winter wheat sown area statistic in sample units.

III. RESULT AND ANALYSIS

A. The accuracy analysis of sample observation under the way of ground survey and remote sensing survey The accuracy of sample observations is related to the

overall extrapolation precision. Table 1 gives the result of sample sown area of winter wheat in the study area based on ground survey and remote-sensing survey to check the truth and accuracy of sample observations based on ground surveys and remote-sensing survey. As seen from the table, sample accuracy of remote sensing survey is 10 m2 (restricted by the spatial resolution of ALOS AVNIR-2 images) and ground survey accuracy is up to 1 m2, which indicate that sample accuracy based on ground survey is higher. In addition, except for a few samples, the area for ground survey samples is generally larger than the area for remote-sensing survey. Relative to the area for remote sensing survey, the area for ground survey samples are closer to the statistical area, which can be inferred from the proportion of the area for remote sensing survey and the area for ground survey in plan. When building the initial sampling frame, sampling unit design is competed in the winter wheat sown area. Therefore, the area ratio of other objects in sample units will be lower, showing that sample accuracy based on ground survey is higher. Significance test of difference were conducted with the ground survey results and remote-sensing survey results, t(11)=-1.969<t0.05(11)=1.7959,there is no significant differences between them.

B. Correlational analysis of the result of ground survey and remote sensing survey for sample: To make a quantitative analysis on the correlativity

between ground survey result and remote sensing survey result of winter wheat area in the study area and provide a basis for building statistical estimator of sampling to extrapolation population. Fig. 3 draws a scatter plot of ground survey result and remote sensing result of sampling ground of winter wheat sown area. As you can see from Fig. 3, it was linear correlation and significance test has been done for the regression equation. F(1,10)=15.207>F0.01(1,10)=10.04 shows that the correlation between ground survey result and remote sensing result about winter wheat acreage was very remarkable. In addition, from the regression equation(y=1.1062x (R2=0.777)) shows that it was linear positive correlation.

C. The efficiency Comparison of population extrapolation based on multiple estimators This research gives the evaluation of the extrapolation

efficiency and provides the solution for improving extrapolation efficiency of crop sown area at the regional scale, by comparing 3 kinds of estimators of extrapolation population. Table 2 shows the results of total area and error estimation. It can be seen from the table that ratio estimator

and regression estimator are more accurate (relative errors are 11.01% and 13.01% respectively) and stable (CVs are 6.20% and 8.04% respectively) relative to the simple estimator (relative error and coefficient of variation (CV) are 34.91% and 9.61% respectively), indicating that we can get higher efficiency of extrapolation by using the ratio estimator and regression estimator with the remote sensing image as auxiliary variable. In addition, under the experimental condition, ratio estimator has higher accurate and stable through comparing ratio estimator with regression estimator. To be sure, Extrapolation relative error is still higher in spite of using 3 kinds of estimators to extrapolate winter wheat sown area (more than 10%). The main reason is that sample size of the design is lower. The sampling ratio in this study is just 0.21% and the total capacity is 5783, i.e. divide mean area for ground survey sample by total study area.

Fig. 3. scatter plot of sample winter wheat area based on ground survey and sensor sensing survey

TABLE I. THE RESULTS OF GROUND AND SENSOR SENSING SURVEY FOR SPATIAL SAMPLING OF WINTER WHEAT SOWN AREA

No Statistical

Area （m2）

The area for remote sensing survey（m2）

The area for ground survey（m2）

The proportion of the area for remote sensing survey in

Statistical area （%）

The proportion of the area for ground survey

in plan （%）

1 578749.12 362800.00 548470.38 62.69 94.77

2 311910.10 265000.00 293638.72 84.96 94.14

3 406353.13 252600.00 365182.48 62.16 89.87

4 426009.93 359600.00 400783.99 84.41 94.08

5 395564.47 385600.00 380576.00 97.48 96.21

6 319674.34 261900.00 299451.80 81.93 93.67

7 429494.42 407000.00 391385.75 94.76 91.13

8 491420.89 448300.00 471567.61 91.23 95.96

9 278183.32 270400.00 265859.51 97.20 95.57

10 271563.80 262400.00 224652.94 96.63 82.73

11 257823.23 239500.00 243794.42 92.89 94.56

12 292311.59 240000.00 286387.12 82.10 97.97 a. Note: statistical area of sample in the table is the gross area of sample, including the area of baulk, road, swag, fallow, etc.

TABLE II. THE RESULTS OF WINTER WHEAT AREA EXTRAPOLATION POPULATION AND ERROR ESTIMATION BASED ON THREE KINDS OF ESTIMATORS

name sampling ratio （%）

estimator of total value （m2）

standard deviation （m2）

relative error（%）

variable coefficient（%） b

simple estimator 0.21 2010436196 161944955 34.91 9.61

ratio estimator 0.21 1654207641 102556176 11.01 6.20

regression estimator 0.21 1685454239 161694407 13.11 8.04 1.01

IV. CONCLUSION The efficiencies of population extrapolation are evaluated

among multiple estimators quantitatively, thus can provide a solution for improving the extrapolation efficiency of crop planting acreage at the regional scale. Mengcheng County in Anhui Province, China is selected as the study area and winter wheat planting acreage as the study object,3 kinds of estimators (they are simple estimator, ratio estimator and regression estimator, respectively) are constructed by combining the data of winter wheat planting acreage surveyed

by remote sensing and the field investigation data of the sampled units, then 3 estimators are used to extrapolate population values and estimate the sampling errors, results show that:

• The experimental results demonstrate that, the ground survey accuracy of winter wheat planting acreage in the samples is higher than that of remote sensing investigation, but there are no significant differences between the two survey results;

• There is a significant direct proportional relationship between the ground survey results of winter wheat planting acreage in all samples and those of remote sensing investigation;

• The extrapolation efficiency of ratio estimator is the highest (relative error and CV are the minimum), the second is that of regression estimator, and the extrapolation efficiency of simple estimator is the lowest in 3 kinds of estimators. Therefore, the ratio estimator has certain effect on improving the estimation accuracy of winter wheat planting area by remote sensing.

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