This document discusses inverse distance weighting (IDW) interpolation, which is a technique used to estimate unknown values between known data points. IDW assumes that points closer to one another are more alike than distant points. The interpolated value is a weighted average of known points, with the weights being inversely proportional to the distances. This allows for the creation of continuous surfaces like elevation or temperature from point data. A case study examines the relationship between weekly rainfall patterns and dengue outbreaks in Sri Lanka using IDW and GIS tools to model spatial and temporal associations and identify potential risk areas.

1. INVERSE DISTANCE
WEIGHTING
BY,
K. P. VINEETH
K. SRI TEJA
D. RAGHUVEER

2. Interpolation
• Interpolation is the process of estimating unknown values that fall between
known values.
In this example, a straight line passes through two points of known value. You
can estimate the point of unknown value because it appears to be midway
between the other two points. The interpolated value of the middle point could
be 9.5.

3. •Used to create continuous surfaces
(rasters) of elevation, rainfall, temperature,
chemical dispersion, or other spatially-
based phenomena.
•The output of interpolation:
Raster – most frequent
Triangular Irregular Network (TIN) -sometimes
• Many interpolation methods: Inverse
Distance Weighted, Spline, Nearest
Neighbour and Kriging.

4. Interpolation: Why should you?
• More realistic representation of a
geographic phenomenon.
• Point data (measurements) may
be all that you can obtain
• Less expensive to collect
• Not possible to measure infinitely small units

5. Interpolation: What Happens
• Point dataset of known
rainfall-level values
• Raster interpolated
from these points
Unknown values are estimated with a
mathematical formula that uses the values
of nearby known points.

6. Inverse Distance Weighting
• Inverse Distance Weighting (IDW) is one of the interpolation
techniques. It explicitly implements the assumption that things that
are close to one another are more alike than those that are farther
apart.
• To predict a value for any unmeasured location, IDW will use the
measured values surrounding the prediction location.
• IDW assumes that each measured point has a local influence that
diminishes with distance. It weights the points closer to the
prediction location greater than those farther away, hence the name
inverse distance weighted.

7. • Weight of each sample point is an inverse proportion to the distance.
IDW is given by
Where,
Zi is value of known point
dij is distance to known point
Zj is the unknown point
n is a user selected exponent

8. Example:

9. Advantages
• Most easily understood.
• Will not produce estimated values outside measurements.
Disadvantages
• No assessment of prediction errors.
• Produces “bulls eye” around data locations.
• The best results from IDW are obtained when sampling is sufficiently
dense with regard to the local variation you are attempting to simulate.
If the sampling of input points is sparse or uneven, the results may not
sufficiently represent the desired surface.

10. Factors affecting interpolated surface
• Size of exponent, n affects the shape of the surface larger n means the closer
points are more influential.
• A larger number of sample points results in a smoother surface.
USAGE
• Methods for spatial prediction to estimate values at unsampled point locations
which could be of interest.
• Time and money are limited; safety and accessibility restrictions .
• Small subsets of object, points or raster cells for estimating the total population.
• Loss of parts of collected samples (recovery) or unsuitability, obvious outlier
points or just for closing “gaps” .
• Prediction of variables at unmeasured locations based on a sample at known
locations .

11. • Creation of surfaces of continuous values .
Examples: Temperature, productivity, elevation, population density .
• Involves the estimation of variables at unsampled locations.

12. • Estimates are based at least in part on other variables .
Examples: Elevation to better estimate temperature due to known
influences .
• Area that characterizes high values for a variable / event (high use,
density, probability of occurrence).
• Aim of estimation is to find values for a variable at unknown locations
based on values measured at sampled locations.

13. • Planning important to make the sampling more efficient / accurate.
• Combining sampled values and positions to estimate values at
unmeasured locations.
Comparing with other techniques
• A surface created with IDW will not exceed the known value range or
pass through any of the sample points. IDW is a good interpolator for
phenomena whose distribution is strongly correlated with distance.
• A surface created with Spline can exceed the known value range, but
must pass through all of the sample points.
• Kriging is one of the most complex interpolators. It measures the
relationships between all of the sample points and then predicts the
cell value. A surface created with Kriging can exceed the known value
range, but does not pass through any of the sample points.

14. CASE STUDY
• The control of vector-borne diseases presents a major challenge to
global health officials. According to the World Health Organization,
every year hundreds of millions people suffer from malaria, dengue
fever, yellow fever and Japanese encephalitis.
• During the recent years, a significant rise in the number of dengue
cases were reported in some geographic regions (outbreak),
particularly in tropical Africa, Central America and Asia.
• Expansion within the countries as well as new dengue outbreaks in
other parts of the world have been receiving considerable attention
by international bodies.

15. • According to the WHO, some 2500 million people are now at risk
of dengue which is about 2/5 of world population.
• Spatial information techniques such as Geographic Information
Systems (GIS), remote sensing and spatial statistics not only allow
researchers to identify and model these disease patterns but also
to help examine the association between climate, climate
variability and vector-borne diseases.
• There were two important trends related to dengue outbreaks in
Sri Lanka: the total number of reported dengue cases was
significantly increased, and dengue started to appear in the
districts outside the western province.

16. • One of the tasks has been the use of modern spatial information
technologies such as Geographical Information Systems and remote
sensing to improve the monitoring and surveillance, understanding
the control factors and explore potentials of predicting disease
outbreaks.
• This study examines the weekly rainfall patterns and dengue
outbreaks in the western province of Sri Lanka between 2000 and
2004.

17. Specifically, this research attempts to answer three questions:
• What is the association between rainfall variability and dengue
outbreaks in the western province of Sri Lanka?
• How do we model the association between spatial and temporal
patterns of rainfall and dengue to predict the outbreaks?
• What are the potential risk areas for dengue outbreaks?

18. Spatial Distribution of Rainfall and Dengue Incidence: Western Province

19. Spatial Distribution of Dengue Transmission Risk

20. CONCLUSION
• There are different methods of interpolation. Choosing an
interpolation method is influenced by your knowledge and the
surface you are modelling. Each method works differently, but most
utilize the concept of spatial autocorrelation; near things are more
alike than things far away.
• IDW method is helpful to create a surface from which we can know
how much area is being influenced. But if we consider point data we
cannot find the influenced area. So, we can use this technique.

21. REFERENCES
• Sumith Pathirana, Masato Kawabata, Rohitha Goonatilake (2009)
“Study of potential risk of dengue disease outbreak in Sri Lanka using
GIS and statistical modelling” Journal of Rural and Tropical Public
Health.
• http://resources.arcgis.com/en/help/main/10.1/index.html#//00310
000002m00000
• http://paulbolstad.cfans.umn.edu/Courses/FR3131/LecSupp/Interpol
ation_3131.pdf
• http://webapps.fundp.ac.be/geotp/SIG/InterpolMethods.pdf