Spatial Interpolation

1. Presented by
Muhammad Safdar

2. Outline
 Introduction of A Study Area
 Interpolation
 Spatial Interpolation & Methods
- Spline
- Inverse Distance Weighting(IDW)
- Kriging
 Methodology
- Study site
 Data Collection Process & Representation Tools
 Results
 Conclusion

3. Introduction of A Study Area
 In a pilot Area of Caracas, Venezuela
 Frequency range of 100 kHz to 6 GHz
 Taking 35 samples per second during a 6
minutes , 206 measurements points
 Data points spaced approximately 100m
from each other is fixed over the 2.64km2
pilot area

4. Interpolation?
 Interpolation is a method of constructing
new data points within the range of a
discrete set of known data points.

5. Spatial Interpolation?
 Interpolation predicts values for cells in a raster from a
limited number of sample data points. It can be used to
predict unknown values for any geographic point data:
elevation, rainfall, chemical concentrations, noise levels,
and so on.

6. Spatial Interpolation Methods
1.Spline
 method estimates values using a mathematical function
that minimizes the total surface curvature, resulting in a
smooth surface that passes exactly through the
sampled points
2.Inverse Distance Weighting(IDW)
• is based on the assumption that the nearby values
contribute more to the interpolated values than
distant observations.
3. Kriging
 depends on spatial and statistical relationships to
calculate the surface.

7. Methodology
Study Site.
The measurements were taken in a pilot zone of Caracas,
Venezuela(Figure 1)with an approximate area of 2.64km2,
which represents 0.609% of the total geographical area of
the Caracas. A total of 206 measurements points, were
selected over the pilot zone. This area is characterized by
a dynamic economic-business activity which is evident
given the presence of shopping centers, office buildings of
the national telephone operators and other
telecommunications companies. On the other hand, this
area also boasts a large number of hospitals and schools,
which is of interest to know the impact of electromagnetic
fields.

9. Data Collection Process
 Time considerations :
Measurements were taken over a period of 30 days, from
February 15th to March 15th of 2010. Measurements
were performed only on working days (from Mondays
to Fridays).Each measurement was taken between
8:00 am and 5:00 pm.
 Geographical considerations:
each measurement point geographical coordinates were
taken using a GPS navigation unit.
 Measurement considerations:

10. Data Process and Representation Tools
 Two informatics tools
1: GvSIG 1.9
2: Past 2.02. GvSIG is a Geographic Information
System (GIS)
Both free software tools distributed under the
GNU/GPL license.

11. Results
Magnitude. (a) IDW, (b) SPLINES, (c) KRIGING.

12. .
Table 1. Results of the measures of ¯t applied to the interpolation
methods.
MEASURES MAE MSE
D (V/m)
Max Error Min Error
OF FIT (V/m) (V/m)
2
(V/m) (V/m)
IDW 0.17 0.05 1.01 0.55 0.008
KRINGING 0.74 0.73 3.81 1.66 0.111
SPLINE 0.89 1.11 4.71 1.98 0.034

13. .
AverageMagnitud
e(V/m)
EstimatedElectricField
Comparison of Spatial Interpolation Methods IDW, KIRGING and SPLINE
for Estimation of Average Electric Fiels Magnitude
3
2.5
2
1.5
1
0.5 Perfect prediction
IDW Method
KRIGING Method
SPLINE Method
Upper acceptance limit
0 Lower acceptance limit
0 0.5 1 1.5 2 2.5 3
Measured Electric Field Average Magnitude (V/m)

14. .

15. .

16. Conclusion
This study has shown that IDW interpolation
method is most likely to produce the best
estimation of a continuous surface of the
average magnitude of electric field intensity.
The IDW method exactness was superior to
the one shown by the SPLINES and
KRIGING techniques.

17. Thanks
Questions?