Inverse distance weighting
Introduction
Inverse distance weighting (IDW) is a type of interpolation method that is commonly used in the field of geostatistics and GIS. The technique is based on the assumption that things that are close to one another are more alike than those that are farther apart. This is often referred to as the first law of geography. IDW is a deterministic method for multivariate interpolation with a known scattered set of points. The assigned values to unknown points are calculated with a weighted average of the values available at the known points.
Methodology
The IDW algorithm is based on the concept of Euclidean distance. The basic premise is that the interpolating surface should be influenced most by the nearby points and less by the distant points. Therefore, each measured point has a local influence that diminishes with distance. The weight is a function of inverse distance. The closer points are given higher weightage and influence the interpolated values more than the farther points.
The general form of the IDW method can be expressed mathematically as follows:
- Z(x) = ∑ (wi * zi) / ∑ wi
where:
- Z(x) is the interpolated value at location x,
- wi is the weight for the ith observation point, which is a function of the distance between the ith observation point and location x,
- zi is the observed value at the ith observation point.
The weight wi is typically computed as:
- wi = 1 / (d^p)
where:
- d is the distance between the observation point and the location to be interpolated,
- p is a power parameter which determines the significance of observed points on the interpolated values.
Applications
IDW interpolation is widely used in various fields such as environmental science, health geography, mining, civil engineering, and agricultural science. It is used to predict unknown values for any geographic point data, such as rainfall levels, chemical concentrations, noise levels, and so on. It can also be used in creating surface analyses for the purposes of contour mapping, landscape analysis, and surface representation.
Advantages and Disadvantages
Like any other interpolation methods, IDW has its own advantages and disadvantages. One of the main advantages of IDW is its simplicity and ease of implementation. It is a deterministic method which means that it will produce the same result each time it is run with the same input data. It is also a flexible method as the power parameter can be adjusted based on the specific requirements of the analysis.
However, IDW has several disadvantages. It assumes that the variable being estimated decreases in influence with distance from its sampled location, which may not always be the case. It also assumes that the spatial distribution is uniform, which is often not the case in nature. It does not take into account potential spatial trends or the direction of spatial correlation. Moreover, it is sensitive to the choice of power parameter and the configuration of the sample points.