accuracy assessment of sampling designs for surveying heavy metal content in soil using sssi aihua...

Accuracy Assessment of Sampling Designs for Surveying Heavy Metal Content in Soil Using SSSI

Aihua Ma;

Jinfeng Wang;

Keli Zhang

2010-05-27

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1. Introduction1. Introduction

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1. Introduction1. Introduction

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Sampling Design ProcessSampling Design Process

2. Methodology2. Methodology

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Sampling Design ProcessSampling Design Process

Soil, food production, land cover type, etc

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Sampling Design ProcessSampling Design Process

N=4×8

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Sampling Design ProcessSampling Design Process

Overall information: variance, the relative error, absolute error

Users on the accuracy of sampling results

2

nV

V

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Sampling Design ProcessSampling Design Process

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Sampling Design ProcessSampling Design Process

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Sampling Design ProcessSampling Design Process

X d variance

Independent samples

Non-independent samples

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Sampling Design ProcessSampling Design Process

Traditional models

Spatial models

Relative error

Coefficient of variation

Design effect

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3. Case Study3. Case Study

County of Zhongyang

County of Jiaokou

two counties Zhongyang and Jiaokou of Shanxi Province were selected as research area, they are high incidence areas of birth defects.

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I use the soil samples as sampling data, soil samples were collected in most of villages, there are 84 points in all.16 kinds of elements in the soil were measured: Al ， As ， Ca ， Cu ， Fe ，K ， Mg ， Mo ， Na ， Ni ， Pb ，Se ， Sn ， Sr ， V ， Zn. Mo element is selected.

3.1The spatial distribution graph of data3.1The spatial distribution graph of data

3. Case Study3. Case Study

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3.2 Data Exploratory analysis3.2 Data Exploratory analysis

Mo semi-variogram

mainly semi-variogram analysis semi-variance function graph can detect whether they have been measured to be spatial dependent among the samples.

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3.3 Choose stratified index3.3 Choose stratified index

This area has the complex and varied terrains and landforms, four stratified way: soil type, geological surface , geochronology, hierarchical cluster.

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Choose stratified indexChoose stratified index

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Five kinds of sampling model are selected to compare the sampling efficiency .

• simple random sampling model• stratified random sampling model• spatial random sampling model• spatial stratified sampling model• sandwich spatial sampling model

3.4 Choose sampling models3.4 Choose sampling models

Traditional models

Spatial models

Systematic model

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3.5 Choose efficiency indicator3.5 Choose efficiency indicator

3.5.1 relative error

Relative error ( )compares the difference between sample mean and its true mean, so the estimated relative error is defined as:

YyYdr /

where = sample mean

= observable population mean

y

Y

rd

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3.4 Choose efficiency indicator3.4 Choose efficiency indicator

3.5.2 Coefficient of variation

100]/)([var yysiationtofcoefficien

nsys /)(

3.5.3 design effect

Design effect is the ratio of estimated variance obtained from the (more complex) sample to the estimated variance obtained from a simple random sample of the same number of units .

The coefficient of variation is a statistical measure of the dispersion of data points in a data series around the mean. It is calculated as follows: The coefficient of variation is a statistical measure of the dispersion of data points in a data series around the mean. It is calculated as follows:

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4. Conclusion4. Conclusion

With smaller sample sizes, the simple random sampling model <stratified sampling model, and the interval is large . With larger sample sizes, the stratified sampling model fluctuates within a certain range, but is more accurate than the simple sampling random model

relative error

0

0. 05

0. 1

0. 15

0. 2

0. 25

0. 3

0. 35

0. 4

10 20 30 40 50 60 70 80sample size

rela

tive

err

or（

%）

simple random model

stratified model

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The sandwich spatial sampling model is the newest method in the SSSI software. It has the same accuracy to the spatial stratified sampling, but it refers to report layers, which can be any unit, for example, a county border, provincial boundary, watershed, or artificial grid

Report layers Stratified by soil type

stratified by geochronology

Administrative villages 0.180 0.085grid 0.066 0.052

Mo

We can see from the table, the relative errors are small, the sampling accuracy are high.

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Coefficient of variationMO 元素

0

1

2

3

4

5

6

7

8

9

10 20 30 40 50 60 70 80sample size

CV

(%)

simple random model

spatial simple random model

sratified model

spatial stratified model

Soil type

0

1

2

3

4

5

6

7

8

9

10 20 30 40 50 60 70 80sample size

CV

(%)

simple random model

spatial simple random model

sratified model

spatial stratified model

Geological surface

0

1

2

3

4

5

6

7

8

9

10 20 30 40 50 60 70 80sample size

CV

(%)

simple random model

spatial simple random model

sratified model

spatial stratified model

geochronology

0

1

2

3

4

5

6

7

8

9

10 20 30 40 50 60 70 80sample size

CV

(%)

simple random model

spatial simple random model

sratified model

spatial stratified model

hierarchical cluster

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Coefficient of variation

0

0. 5

1

1. 5

2

2. 5

1 2 3 4 5 6 7 8sample size

CV

(%)stratified by soiltype

stratified by geochronology

It shows which stratified method is more efficient, Stratification by soil type yields higher accuracy than by geochronology in the case of smaller sample sizes, but lower accuracy in larger sample sizes.

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design effect

1.设计效应1.设计效应

models

Sample

sizes

SrsStrRs

(a)

SStrs

(a)

StrRS

(b)

SStrs

(b)

10 0.945 0.891 0.143 0.899 0.228

20 0.664 0.964 0.187 0.798 0.133

30 0.557 0.801 0.230 0.745 0.100

40 0.485 0.719 0.241 0.661 0.070

50 0.430 0.664 0.244 0.556 0.059

60 0.392 0.536 0.209 0.469 0.048

70 0.361 0.402 0.177 0.351 0.043

80 0.338 0.203 0.152 0.092 0.096

models

Sample sizes

StrRs

(c)

SStrs

(c)

StrRS

(d)

SStrs

(d)

10 0.931 0.172 0.889 0.261

20 0.788 0.228 0.901 0.252

30 0.710 0.203 0.776 0.281

40 0.606 0.178 0.692 0.225

50 0.523 0.156 0.612 0.193

60 0.405 0.127 0.474 0.150

70 0.293 0.106 0.359 0.137

80 0.150 0.087 0.155 0.101

MO

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6. discussion6. discussion

Efficiency is up to: Sampling models Stratified method

Future work Sample with layout

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Thanks!