Upload
quentin-elliott
View
215
Download
0
Tags:
Embed Size (px)
Citation preview
Accuracy Assessment of Sampling Designs for Surveying Heavy Metal Content in Soil Using SSSI
Aihua Ma;
Jinfeng Wang;
Keli Zhang
2010-05-27
Website : www.sssampling.org 2
Website : www.sssampling.org 3
1. Introduction1. Introduction
Website : www.sssampling.org 4
1. Introduction1. Introduction
Website : www.sssampling.org 5
Sampling Design ProcessSampling Design Process
2. Methodology2. Methodology
Website : www.sssampling.org 6
Sampling Design ProcessSampling Design Process
Soil, food production, land cover type, etc
Website : www.sssampling.org 7
Sampling Design ProcessSampling Design Process
N=4×8
Website : www.sssampling.org 8
Sampling Design ProcessSampling Design Process
Overall information: variance, the relative error, absolute error
Users on the accuracy of sampling results
2
nV
V
Website : www.sssampling.org 9
Sampling Design ProcessSampling Design Process
Website : www.sssampling.org 10
Sampling Design ProcessSampling Design Process
Website : www.sssampling.org 11
Sampling Design ProcessSampling Design Process
X d variance
Independent samples
Non-independent samples
Website : www.sssampling.org 12
Sampling Design ProcessSampling Design Process
Traditional models
Spatial models
Relative error
Coefficient of variation
Design effect
Website : www.sssampling.org 13
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.
Website : www.sssampling.org 14
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
Website : www.sssampling.org 15
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.
Website : www.sssampling.org 16
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.
Website : www.sssampling.org 17
Choose stratified indexChoose stratified index
Website : www.sssampling.org 18
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
Website : www.sssampling.org 19
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
Website : www.sssampling.org 20
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:
Website : www.sssampling.org 21
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
Website : www.sssampling.org 22
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.
Website : www.sssampling.org 23
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
Website : www.sssampling.org 24
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.
Website : www.sssampling.org 25
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
Website : www.sssampling.org 26
6. discussion6. discussion
Efficiency is up to: Sampling models Stratified method
Future work Sample with layout
Website : www.sssampling.org 27
Thanks!