**Operational crop acreage estimation at a national scale based on
statistics and remote sensing**

**Xianfeng JIAO^1^, Heather McNAIRN^1^, Bangjie YANG^2^ Jiali SHANG^1^
Zhiyuan PEI^2^**

**1 Agriculture and Agri-Food Canada, Ottawa, Ontario, Canada K1A 0C6**

**2 Chinese Academy of Agricultural Engineering,**

**Ministry of Agriculture of China**

**41 Maizidian, Chaoyang District, Beijing China 100026;**

**Abstract:** This paper provides an efficient and effective procedure
for operational crop acreage estimation at a national scale. **A**n
innovated approach which incorporates both coarse and finer resolution
satellite data into stratified sampling was presented. The crop planting
area from MODIS data was defined as the sampling population. The
population is divided into non-overlapping strata from which an
independent sample is selected from each stratum. For selected samples
that represent the population, a crop inventory was conducted using
remote sensing imagery with finer resolution. At a certain confidence
level, crop acreage could be estimated over the entire survey area. The
method has been adopted by the Ministry of Agriculture of China for
paddy rice inventory in northeast of China in 2005.

# 1 Introduction

Crop acreage is the determining factor in crop production. Monitoring
and estimating crop acreage at a national scale is required in order to
determine the national or regional food demand and supply balance, and
to gauge social security. Whether during times of world food shortages,
or during periods of surplus, monitoring and estimating crop acreage
requires long-term efforts. Crop acreage estimation using remote sensing
provides timely and reliable information. Since 1983, remote sensing has
been considered the key technology for estimating crop acreage and China
has made significant progress in the application of this technology.
Initially, remote sensing monitoring over the important cropping regions
within China was the primary approach for crop monitoring and
estimating. Since 1999 The Chinese Academy of Agricultural Engineering
(CAAE), Ministry of Agriculture of China (MOA), has delivered,
operationally, crop area estimates over the main grain production
regions using inputs of Earth observation (EO) data. Using this remote
sensing approach, annual crop acreage estimates are provided across
China for wheat, corn, soybean, cotton and rice. However, such an
approach poses many challenges. Crop acreage estimated over these
selected regions must be extrapolated to provide crop acreage
information for the entire country.

This paper introduces a new sampling approach based on statistics and
remote sensing and discusses progress to date on integrated SAR and
optical imagery for crop classification and acreage estimation. The
method was applied to paddy rice acreage estimation in the northeast of
China.

# 2 Methodology

Monitoring and estimating crop acreage at a national scale presents
specific problems with respect to data acquisition and method
development.

1)  Data acquisition: It is impractical to acquire remote sensing
    imagery over all of China during the crop growing season. Processing
    such large quantities of imagery to support operational reported is
    not feasible. Adverse weather conditions during critical crop
    growing period limits the availability of remote sensing imagery. In
    particular, humid and rainy conditions during the growing season
    make the acquisition of optical remote sensing imagery problematic.
    For an operational monitoring approach, the availability of
    satellite data must be assured. Complementary crop information can
    be gained through integrating optical data and synthetic aperture
    radar (SAR) data from satellites such as ASAR and RADARSAT. These
    sensors offer the advantage of collecting information under cloudy
    sky conditions. Consequently a multi-sensor (optical and SAR)
    approach provides a practical solution for operational crop
    monitoring activities.

2)  Method development: Some approaches to estimate crop acreage are
    capable of achieving high accuracies using EO data. However, not all
    crops are always well classified. For example, winter wheat acreage
    estimation using NDVI from Landsat TM in Northern China has achieved
    high accuracies. But this method is not transferable to the crops of
    southern China, neither to other crops grown in northern China. On
    the other hand, some methods have been successfully applied for
    small area mapping, but achieved poor results or where not
    applicable at the national level. In China, crop planting and
    harvesting times are concentrated in the period from April to
    October each year. Before crops are harvested, reports on crop
    acreage must be submitted, making for tight timelines to process and
    analyze data. Thus the methods adopted for national crop estimation
    must be effective and efficient.

> In this study, an innovative sampling approach was developed by
> incorporating coarse resolution MODIS and high resolution Landsat TM
> satellite data in a statistical stratified sampling. The method was
> developed to estimate paddy rice acreage in the northeast of China. In
> the northeast of China paddy rice acreage has fluctuated considerably
> during the past 10 years. Monitoring paddy rice acreage is meaningful
> for estimating grain production.
>
> The paddy rice planting area in the current year was defined as the
> sampling population. Paddy rice mapping was conducted using MODIS data
> over the entire northern China to obtain an overview of the current
> year's paddy rice planting. Because of the spatial resolution of MODIS
> data, the resulting information is coarse and does not satisfy the
> requirements of official annual crop reports. A further detailed crop
> inventory using high spatial resolution remote sensing imagery is
> needed. Standard 1:50,000-scale topographic maps were chosen as the
> sampling unit. At a 95% level of sampling accuracy, the population was
> divided into 6 strata according to the method of accumulated square
> root. The sample was then taken from each of these strata using
> proportionate allocation. For selected samples that represent the
> population, the crop inventory was conducted using Landsat TM and
> ENVISAT ASAR imageries. At a 95% confidence level, annual paddy rice
> acreage over the entire northeast of China was estimated.

# 3 stratified sampling design

## 3.1Population definition

In statistics, population refers to the total set of observations that
can be made. In this study, the purpose of the implementation survey is
to estimate paddy rice acreage across the whole northeast of China. The
population was defined as the area of planted paddy rice. In northeast
of China, paddy rice acreage fluctuates significantly every year, and
paddy fields rotate frequently. Thus planting acreage is not available
from historical databases. MODIS has a wide viewing swath and
high-frequency revisits, making it an ideal instrument to provide an
initial overview. Using MODIS Surface Reflectance 8-Day Global 250m
data, the Normalized Difference Vegetation Index (NDVI), Vegetation
Condition Index (VCI), Enhanced Vegetation Index (EVI) and Land Surface
Water Index (LSWI) were calculated. These vegetation indices were used
to capture the crop spectral characteristics. Through knowledge-base, a
stepwise removal model was designed to automatically identify paddy
rice. The resulting paddy rice planting area was defined as the
population. The distribution rice paddies is shown in Figure 1.

![](media/image1.png){width="3.0in"
height="3.9374015748031495in"}![](media/image2.png){width="3.0in"
height="3.9374015748031495in"}

## 

## 

## 3.2 Sampling frame 

The main characteristic of a crop acreage survey is that the sampling
population is an area in which the sampling units are small parts of
that area. When the population is finite, the frame may be defined by an
explicit list of its elements. The sampling unit was considered as the
area of a standard 1:50000-scale topographic map. This kind of sampling
unit has certain advantages. A specific code is available for every unit
and there is no area overlap, as compared with a sampling unit defined
as a set area or satellite image frame. In this study, the population
was defined as the current year's paddy rice planting area. The sampling
frame, which is the list of standard 1:50000-scale maps within the
population, was easy to establish. The sampling frame consisted of 1197
sampling units as shown in Figure 1.

## 3.3 Stratification

The objective of a stratification design is to minimize the variance of
the resulting estimates by creating homogeneous strata of sampling
units. When a stratification design is used, the population is divided
into several strata, and separate random samples are drawn from each
stratum. As the number *L* of strata is concerned, Cochran (1977)
developed a model representing the approximate reduction in the variance
gained over simple random sampling by stratification, and deduced that
there is little to be gained from having more than six strata.

In this study, the population was stratified into six strata. Once the
sampling frame is established, the Cumulative Square Root of the
Frequency (CSRF) was used. This is the preferred method to establish
strata boundaries.

The cumulative root frequency procedure of stratum construction is
carried out for the division of population into *L* strata as follow:

1)  Define the stratification variable X as paddy rice planting area
    within sampling unit;

2)  Arrange the stratification variable *X* in ascending order;

3)  Group the *X* into a number of classes, *J;*

4)  Determine the frequency for each class $f_{i}$ *(i=1, 2, ...J);*

5)  Determine the square root of the frequencies in each class;

6)  Cumulate the square root of the frequencies $\sum_{}^{}\sqrt{f_{j}}$

7)  Divide the sum of the square root of the frequencies by the number
    of strata;

> $$Q = \frac{1}{6}\sum_{}^{}\sqrt{f_{j}}$$

8)  Take the upper boundaries of each stratum to be the *X* values
    corresponding to

> *Q, 2Q, 3Q,......6Q*

###### The statistics of each stratum are given in Table 1. Figure 2 shows the distribution of strata. 

###### 

###### Table 1: The statistics of each stratum

  ------------ ------------- ------------------- -------------------------
  Strata       boundary      Criterion (ha.)     the number of strata

  1            68.92         0-550               482

  2            137.84        550-1500            249

  3            206.76        1500-2950           177

  4            275.68        2950-5100           120

  5            344.59        5100-8400           95

  6            413.51        \>28800             74
  ------------ ------------- ------------------- -------------------------

## 3.4 Proportionate allocation

> The precision and cost of a stratified design are influenced by the
> way that sample elements are allocated to strata. In this study, the
> method of proportionate allocation was adopted to determine the
> sampling fraction which is the proportion of a population to be
> included in a sample. With proportionate stratification, the sample
> size of each stratum is proportionate to the population size of the
> stratum. This means that each stratum has the same sampling fraction.
> Strata sampling sizes are determined by the following equation:

$n_{0} = \frac{N\sum_{h = 1}^{L}{N_{h}s_{h}^{2}}}{V}$$n = \frac{n_{0}}{1 + \frac{n_{0}}{N}}$

Sampling fraction,

$f = \frac{n}{N} = \frac{n_{h}}{N_{h}}$The weight of stratum h, W~h~

$W_{h} = \frac{N_{h}}{\sum_{h = 1}^{L}N_{h}}$

where：

V:The know variance of the population.

L: The number of strata in the population.

N: The number of observations in the population.

N~h~: The number of observations in stratum h of the population ，h=1,
2, .... L

n: The number of observations in the sample.

n~h~: The number of observations in stratum h of the sample ，h=1, 2,
.... L

s~h~: The sample estimate of the population variance in stratum h ,

$S_{h}^{2} = \frac{1}{n_{h} - 1}\sum_{i = 1}^{n_{h}}{(y_{\text{hi}} - {\overline{y}}_{h})^{2}}$

Assuming a 95% sampling accuracy level, from these equations the
sampling fraction is 25%. The population consists of 1197 sampling
units. The total sample is 300 standard 1:50000-scale topographic maps.
According to the proportion of 25%, a simple random sample was drawn
from each stratum. Table 2 shows the number of observations in the
population and in the sample in each stratum and the weight of strata.

###### Table 2: the number of observation in the population and in the sample and the weight 

  ---------- ---------------- -------------- ---------------- --------------
  stratum    the number of    Fraction (%)   the number of    Weight (%)
             observation in                  observation in   
             the population                  the sample       

  1          482              25%            121              40%

  2          249              25%            62               20%

  3          177              25%            44               14%

  4          120              25%            30               10%

  5          95               25%            24               7%

  6          74               25%            19               6%
  ---------- ---------------- -------------- ---------------- --------------

# 4 Crop inventory

This stratified sampling scheme was implemented in a national crop
acreage estimation system in 2005 for paddy rice acreage estimation in
the northeast of China. Following the stratified sampling method, the
total annual crop planting area was defined as the sampling population.
At a 95% level of sampling accuracy, the population was divided into 6
strata according to the method of CSRF. The sample was then taken from
each of these strata using proportionate allocation. For selected
sample, a crop inventory was conducted using remote sensing imageries.
For the most part, TM and SPOT4 images were used for the paddy rice
inventory. Humid and rainy conditions during the growing season created
problems for the acquisition of optical remote sensing imagery. The
amount of available optical data was limited and thus the requirements
of the number of samples determined by stratified sampling could not be
met. Supplemental imagery can be acquired from SAR sensors such as ASAR
and RADARSAT. These sensors offer the "all-weather" advantage. An
optical-SAR approach provides a practical solution for crop acreage
estimation at a national scale.

## 4.1 Data collection

Seven optical and two radar satellite images were collected during the
2005 growing season. Two alternating polarization mode precision images
of ASAR with nominal resolutions of 25 m were collected. The alternating
polarization was HH/VV, and the imaging modes were IS1 and IS6. SPOT-5
XS data have very high spatial resolution. These data were used to
supplement ground data collection and for validation of the
classification results. Sample images covering the study sites are shown
in Figure 3.

![](media/image3.png){width="3.0076388888888888in" height="4.25in"}

Ground truth data were collected to support the crop classification
through on-site surveys. Each sample site covers an area of 500m by 500m
and includes several fields with various crop types. Field boundaries
were digitized using a Trimble DGPS. The recorded field observations
included crop type and crop distribution.

## 4.2 Image pre-processing 

All images were ortho-rectified and co-registered to the same map
projection and pixel size (30 m). Cloud and heavy haze were masked out
manually and were not included in the training and testing samples. For
the purposes of crop classification, atmospheric correction does not
positively affect the results (McNairn et al., 2007), thus the TM and
SPOT imagery was used without atmospheric correction. The ASAR imagery
was filtered using two passes of a 3 by 3 Gamma filter to reduce speckle
effects.

## 4.3 Image classification

> Ground truth data combined with visual interpretation from the August
> 9 SPOT-5 image were used as training and testing sets for supervised
> classification. For each crop, half of the fields were randomly
> selected for training the classifier and the second half were reserved
> for testing the classification accuracy. The training pixels and
> testing pixels were selected from different fields.

From an operational perspective, crop classification methods must be
effective and efficient. The methods should be consistent and must be
easily implemented. Some methods have high accuracies over local smaller
sites, but costs and processing demands make them unattractive for
larger regions. In this study, a decision tree (DT) classification
method was used. A DT establishes a hierarchical system of rules to
optimally separate classes based on linear discriminate functions
estimated from the training data. The DT approach was developed by
Agriculture and Agri-Food Canada (AAFC) based on the See5 software.

Independent samples were used to test crop classification accuracies.
The accuracy of the classification was determined by comparing the test
set with the classification results to generate producer's, user's and
the overall accuracies.

At the individual class level, one encouraging observation is that using
a single-date image, either optical or radar, a high classification
accuracy can be achieved for the paddy rice class. Rice grows on flooded
soils. During the rice transplanting period and the early part of the
rice growing season, paddy fields are a mixture of green rice plants and
water. This unique physical feature of paddy rice significantly
contributes to paddy rice discrimination using remote sensing imagery.
Most paddy rice in China grows in warm, humid environments where the
region is always covered by heavy clouds and where significant rainfall
occurs during the paddy rice growing season. Consequently the
application of SAR data is attractive for monitoring paddy rice planting
areas across China.

# 5 Estimation

> For selected samples that represent the population, the crop inventory
> was conducted using remote sensing imagery. After the crop inventory,
> the crop acreage within each sample was acquired. At a certain
> confidence level, crop acreage of the entire survey region could be
> estimated.
>
> In this study, the overall sample mean was used to estimate the
> population mean. To compute the overall sample mean, the following
> equation was used.
>
> An unbiased estimator of the population mean and variance are,
>
> ${\overline{y}}_{\text{st}} = \frac{1}{N}\sum_{h = 1}^{L}n_{h}{\overline{y}}_{h} = \sum_{h = 1}^{L}W_{h}{\overline{y}}_{h} = \sum_{h = 1}^{L}W_{h}\frac{1}{n}_{h}\sum_{i = 1}^{n_{h}}y_{\text{hi}} = \frac{1}{n}\sum_{h = 1}^{L}{\sum_{i = 1}^{n_{h}}y_{\text{hi}}}$
>
> And
>
> $V_{\text{st}}(\overline{y}) = s^{2}(\overline{y}) = \sum_{h = 1}^{L}\frac{W_{h}^{2}s_{h}^{2}}{n_{h}} - \sum_{h = 1}^{L}\frac{W_{h}s_{h}^{2}}{N} = \frac{1 - f}{n}\sum_{h = 1}^{L}W_{h}s_{h}^{2}$
>
> Where
>
> ${\overline{y}}_{h} = \frac{1}{n_{h}}\sum_{i = 1}^{n_{h}}y_{\text{hi}}$

$s_{h}^{2} = \frac{1}{n_{h} - 1}\sum_{i = 1}^{n_{h}}{(y_{\text{hi}} - {\overline{y}}_{h})^{2}}$

L: The number of strata in the population

*n~h\ ~*~:~The number of observations in stratum h of the sample ，h=1,
2, .... L，

*~yhi~*: Paddy rice acreage in stratum h of the sample i

*W~h~*: the stratum weight in acreage in stratum h

This stratified sampling was implemented in 2005 for paddy rice acreage
estimation in northern China, with the integration of optical and SAR
imagery. The result of this survey is an estimated 3.9% increase over
last year's paddy rice acreage.

# 6 Summary 

The stratified sampling scheme proposed in this paper entails first
defining the crop planting area from MODIS data as the sampling
population and then establishing a sampling frame, choosing the area of
a standard 1:50000-scale topographic map as the sampling unit. Finally,
the population is divided into non-overlapping strata from which an
independent sample is selected from each stratum. For selected samples
that represent the population, a crop inventory was conducted using
remote sensing imagery. At a certain confidence level, crop acreage
could be estimated. The annual crop acreage at a national or regional
scale can be obtained by implementing this stratified sampling. This
study provides an efficient and effective procedure for operational crop
acreage estimation at a national scale.

This study has demonstrated that integration of SAR data with optical
imagery can support crop classification and can provide a practical
means of acquiring enough imagery to satisfy the demands of a stratified
sampling approach. SAR sensors, such as RADARSAT and ASAR, permit the
collection of data under cloudy conditions and adds some additional
information for differentiating specific crop types, in particular paddy
rice.

According to sampling theory, a stratified sampling can provide greater
precision than a simple random sample of the same size. Because it
provides greater precision, stratified sampling often requires a smaller
sample and requires fewer resources. In this study, not only was the
stratified sampling investigated, but an innovated approach which
incorporates both coarse and finer resolution satellite data into
stratified sampling was presented. This procedure takes full advantage
of the characteristics of sampling theory and remote sensing technology.

**Acknowledgements**: the authors would like to thank the team at
Chinese Academy of Agricultural Engineering (CAAE), for collecting the
ground truth data and processing the remote sensing data.

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