Geo-statistical Methods For Spatial Interpolation in GIS

Transcription

International Conference on Space (ICS-2014) Organized by
SUPARCO, IST, and ISNET
12-14 Nov 2014, Islamabad
Geo-statistical Methods For
Spatial Interpolation in GIS
Anam Ahsan1, Shahid Parvez2
1B.S
(Hon.) student, Dept of Space Science, University of the Punjab, Lahore <anamahsan33@yahoo.com>
2Assist Prof, Dept of Space Science, University of the Punjab, Lahore <shahid.spsc@pu.edu.pk>
www.pu.edu.pk
Contents
 Study Objective
 Study Area
 Geo-statistical Analyses in ArcGIS
• Modeling
• Kriging and its Types
Spatial Interpolation in New-LocClim
 Comparison
 Conclusions
 References
Study Objectives
• To understand Kriging and its Types.
• To investigate interpolation of Temperature values for
unknown places using Kriging.
• To examine the comparison of Kriging in ArcGIS and
New-LocClim (FAO).
Study Area
(Temperature Data of Some Cities of Pakistan)
Arabian Sea
Sample data - Temperature
City/Town
Abbotabad
Bahawalnagar
Bahawalpur
Chaman
Charsadda
Chilas
Daska
Digri
Faisalabad
Gagai
Gupis
Hyderabad
Islamabad
Jhelum
Jhang
Karampur
Kharan
Karachi
Kasur
Lahore
Longitude (Deg)
Latitude (Deg)
73.21
73.25
71.68
66.45
71.73
74.09
74.35
69.11
73.07
64.70
73.44
68.36
73.06
73.72
72.31
73.69
65.41
67.02
74.44
74.34
34.15
29.99
29.39
30.91
34.15
35.42
32.33
25.15
31.41
29.29
36.22
25.37
33.71
32.93
31.26
30.28
28.58
24.89
31.11
31.54
Source: http://www.accuweaddzther.com
High
Temperature (˚C)
32
40
40
37
32
32
34
34
34
34
30
34
32
32
34
40
34
34
34
34
Low
Temperature (˚C)
20
26
26
20
30
20
27
29
27
29
19
29
30
30
27
26
29
29
27
27
Parameters and Histogram
High Temperature
Histogram
Formula Calculation
14
Mean
34.87
12
Median
34.00
Mode
34.00
Minimum
30.00
Maximum
40.00
34
Frequency
Parameter
10
32
8
38
6
40
4
2
30
0
0
Temperature (˚C)
Low Temperature
Mean
Median
Formula
Calculation
25.53
27.00
12
27
10
Frequency
Parameter
Histogram
21
8
29
6
Mode
20.00
Minimum
19.00
2
Maximum
30.00
0
31
4
19
1
2
0
0
3
4
5
Temperature (˚C)
6
7
Geo-Statistics
Geo-statistics
•
•
Geo-statistics is a branch of statistics focusing on two
data set :
•
Spatial
•
Spatiotemporal
Geo-statistical analyses of data occur in two phase :
•
Modeling (for semi-variogram or covariance)
•
Kriging (for surface creation)
Modeling
• In modeling the semi-variogram or covariance is use to
analyze surface properties.
Semi-variogram
Kriging
Interpolation
Kriging Interpolation
•
Kriging is a geo-statistical
interpolation.
•
Kriging uses statistical models that allow a variety of
map outputs including predictions, prediction standard
errors, probability, etc.
•
Three types of kriging are normally used:
•
Simple Kriging
•
Ordinary Kriging
•
Universal Kriging
method
for
spatial
Simple Kriging
Simple Kriging
•
It assume that the mean of the data set is known.
•
This assumption is unrealistic in most cases.
Threshold
Flow Chart
(Simple Kriging in Arc-Map)
Geo-Statistical
Wizard
Simple Kriging
Next
Searching
Neighborhood
Next
Semivarogram/
Covariance
Geo-statistical
Model Section
Next
Crossvalidation
Finish
and
Ok
Prediction Map - Temperature
(Simple Kriging in Arc-map)
Contour Values
Attribute
: High Temp
Neighbor : 5
Mean
: -0.03012
RMS
: 2.021
Model
: Exponential
Partial sill : 10.86
Minor range : 5.002
Direction : 287.4
Measured and Predicted Values
(MS Excel work of Simple Kriging)
Measured
Predicted
Error
Std-Error Stdd-Error Norm-Value Source-ID
Included
32.00
32.11
0.11
2.08
0.05
-0.28
0
Yes
40.00
37.93
-2.07
2.55
-0.81
-0.83
1
Yes
40.00
34.99
-5.01
3.08
-1.63
-1.68
2
Yes
37.00
35.40
-1.60
3.03
-0.53
-0.72
3
Yes
32.00
33.66
1.66
1.74
0.96
1.42
4
Yes
32.00
32.20
0.20
2.81
0.07
-0.04
5
Yes
34.00
34.00
0.00
1.81
0.00
-0.36
6
Yes
34.00
34.72
0.72
3.07
0.24
0.12
7
Yes
34.00
35.22
1.22
2.74
0.45
0.95
8
Yes
34.00
34.78
0.78
3.13
0.25
0.20
9
Yes
30.00
33.90
3.90
3.03
1.29
1.68
10
Yes
34.00
34.17
0.17
2.62
0.06
-0.20
11
Yes
32.00
32.40
0.40
2.11
0.19
0.04
12
Yes
32.00
33.54
1.54
2.82
0.55
1.23
13
Yes
Correlation and Scatter plot
Correlation
1
Column 2
0.720794
1
Scatterplot
39.00
Values
Column 1
Column 2
Predicted
Column 1
Data
Point
36.00
Linear
(Data
Point)
33.00
30.00
27.00
32.00
37.00
Measured Values
42.00
Ordinary Kriging
Ordinary Kriging
• Data having a constant mean (no trend) - value is not
known in advance.
• Orange dots show a random error – fluctuate around the
unknown mean.
Flow Chart
(Ordinary Kriging in Arc-Map)
Geo-Statistical
Wizard
Next
Searching
Neighborhood
Ordinary
Kriging
Next
Semivarogram/
Covariance
Geo-statistical
Model Section
Next
Crossvalidation
Finish
and
Ok
Prediction Map - Temperature
(Ordinary Kriging in Arc-Map)
Contour Values
Attribute : High Temp
Neighbor : 5
Mean
: -0.03012
RMS
: 1.708
Model
: Exponential
Minor range : 5.002
Direction : 287.4
Measured and Predicted Values
(MS Excel work of Ordinary Kriging)
Measured Predicted
Error
Std-Error Stdd_Error Norm-Value Source-ID
Included
32.00
33.39
1.39
1.93
0.72
1.23
0
Yes
40.00
38.94
-1.06
1.99
-0.53
-0.83
1
Yes
40.00
37.67
-2.33
2.53
-0.92
-1.23
2
Yes
37.00
36.77
-0.23
2.39
-0.10
-0.28
3
Yes
32.00
33.01
1.01
1.41
0.71
1.08
4
Yes
32.00
31.49
-0.51
2.41
-0.21
-0.45
5
Yes
34.00
33.75
-0.25
1.45
-0.18
-0.36
6
Yes
34.00
34.43
0.43
2.08
0.20
0.12
7
Yes
34.00
34.38
0.38
1.93
0.20
0.04
8
Yes
34.00
34.76
0.76
2.44
0.31
0.53
9
Yes
30.00
32.53
2.53
2.37
1.07
1.68
10
Yes
34.00
33.99
-0.01
1.89
-0.01
-0.12
11
Yes
32.00
32.00
0.00
1.82
0.00
-0.04
12
Yes
32.00
33.09
1.09
1.92
0.57
0.83
13
Yes
Correlation and Scatterplot
Correlation
1
Column 2
0.800989
1
Scatterplot
39.00
Values
Column 1
Column 2
Predicted
Column 1
Data
Point
36.00
Linear
(Data
Point)
33.00
30.00
27.00
32.00
37.00
Measured Values
42.00
Universal Kriging
Universal Kriging
• It assumes there is trend in the data, but the terms of the
trend function are not known in advance.
• The data values (orange dots) are through of as random
errors that fluctuate around the unknown tend.
Flow Chart
(Universal Kriging in Arc-Map)
Geo-Statistical
Wizard
Next
Searching
Neighborhood
Universal
Kriging
Next
Semivarogram/
Covariance
Geo-statistical
Model Section
Next
Crossvalidation
Finish
and
Ok
Prediction Map – Temperature
(Universal Kriging in Arc-Map)
Contour Values
Attribute : High Temp
Neighbor : 5
Mean
: -0.03012
RMS
: 1.862
Model
: Exponential
Minor range : 5.002
Direction : 287.4
Measured & Predicted Values
(Excel work of Universal Kriging)
Measured
Predicted
Error
Std-Error
Stdd-Error
Norm-Value
Source-ID
Included
32.00
32.24
0.24
2.06
0.12
-0.12
0
Yes
40.00
38.55
-1.45
2.34
-0.62
-0.83
1
Yes
40.00
35.83
-4.17
3.03
-1.38
-1.68
2
Yes
37.00
36.34
-0.66
2.92
-0.23
-0.63
3
Yes
32.00
33.41
1.41
1.60
0.88
1.42
4
Yes
32.00
31.65
-0.35
2.71
-0.13
-0.45
5
Yes
34.00
33.82
-0.18
1.63
-0.11
-0.36
6
Yes
34.00
35.10
1.10
2.95
0.37
0.53
7
Yes
34.00
35.17
1.17
2.52
0.46
0.72
8
Yes
34.00
35.73
1.73
3.14
0.55
1.08
9
Yes
30.00
33.32
3.32
2.88
1.15
1.68
10
Yes
34.00
34.12
0.12
2.44
0.05
-0.28
11
Yes
32.00
32.28
0.28
2.06
0.14
-0.04
12
Yes
32.00
33.21
1.21
2.59
0.47
0.83
13
Yes
Correlation and Scatterplot
Correlation
1
Column 2
0.760096
1
Scatterplot
39.00
Values
Column 1
Column 2
Predicted
Column 1
Data
Plot
36.00
Linear
(Data
Plot)
33.00
30.00
27.00
32.00
37.00
Measured Values
42.00
Spatial Interpolation
Using New-LocClim (FAO)
New-LocClim (FAO)
(V 1.10)
• New LocClim is a tool for spatial interpolation of agroclimatic data.
• New LocClim runs in 3 modes:
• Single Point Mode
• Workbench Mode
• Automatic Mode
Sample Data – Temperature
Longitude
Latitude
Average Temperature
City/Town
73.21
34.15
26
Abbotabad
73.25
29.99
33
Bahawalnagar
71.68
29.39
33
Bahawalpur
66.45
30.91
28.5
Chaman
71.73
34.15
31
Charsadda
74.09
35.42
26
Chilas
74.35
32.33
30.5
Daska
69.11
25.15
31.5
Digri
73.07
31.41
30.5
Faisalabad
64.7
29.29
31.5
Gagai
73.44
36.22
24.5
Gupis
68.36
25.37
31.5
Hyderabad
73.06
33.71
31
Islamabad
73.72
32.93
31
Jehlam
72.31
31.26
30.5
Jhang
Flow Chart
New-LocClim (FAO)
Workbench
Mode
Data Source
Import
From file
Setting
(method and
Grid)
Legend
Export
Spatial Interpolation using New-LocClim
Station RMS : 1.945
Grid Size
:3
Grid RMS : 1.358
Scale:
Pakistan
Comparison
Comparison of Kriging in ArcGIS
Simple Kriging
Attribute
: High Temp
Neighbor
:5
Mean
: -0.03012
RMS
: 2.021
Model
: Exponential
Minor range : 5.002
Direction
: 287.4
Ordinary Kriging
Universal Kriging
Contour Values
High Temp
5
-0.03012
1.708
Exponential
10.86
5.002
287.4
High Temp
5
-0.03012
1.862
Exponential
10.86
5.002
287.4
Comparison of Kriging in
ArcGIS and New-LocClim
40 ˚ C
35 ˚ C
30 ˚ C
RMS : 1.708
RMS : 1.945
Conclusions
•
The results indicate that the comparison of Geo-statistical
analyses in ArcGIS and spatial interpolation in New LocClim of
temperature data, Geo-statistical analyses in ArcGIS is better for
interpolation.
•
The correlation of Ordinary Kriging is 0.80 (perfect positive
relationship) and RMS is 1.708, which show that Ordinary
Kriging is better as compared to the other methods.
•
We can not say that only Ordinary Kriging is better than others,
basically it depends on number of data values.
Reference
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• CHANG Wen-Yuan DAI Xin-Gang CHEN Hong-Wu (2004) “A CASE STUDY OF GEOSTATISTICAL
INTERPOLATION IN METEOROLOGICAL FIELDS CHINESE JOURNAL OF GEOPHYSICS” Vol.47, No.6, 2004,
pp: 1104∼1112
• Benjamin J. Mason U.S. EPA (1992). “Preparation of Soil Sampling Protocols: Sampling Techniques and Strategies.”
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• http://www.esri.com/software/arcgis/extensions/geostatistical
Thank you for your kind attention.

Geo-statistical Methods For Spatial Interpolation in GIS

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