INVERSE DISTANCE WEIGHTING

BY,

K. P. VINEETH

K. SRI TEJA

D. RAGHUVEER

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.

•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.

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

Interpolation: What Happens

• Point dataset of known

rainfall-level values

• Raster interpolated

from these points

Unknown values are estimated with amathematical formula that uses the valuesof nearby known points.

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.

• 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

Example:

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.

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 .

• Creation of surfaces of continuous values .

Examples: Temperature, productivity, elevation, population density .

• Involves the estimation of variables at unsampled locations.

• 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.

• 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.

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.

• 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.

• 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.

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?

Spatial Distribution of Rainfall and Dengue Incidence: Western Province

Spatial Distribution of Dengue Transmission Risk

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.

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#//00310000002m00000

• http://paulbolstad.cfans.umn.edu/Courses/FR3131/LecSupp/Interpolation_3131.pdf

• http://webapps.fundp.ac.be/geotp/SIG/InterpolMethods.pdf