What is a spatial
interpolation?

##
1Inverse Distance Weighting (IDW)

**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.**

**Interpolation is based on the assumption that spatially distributed objects are spatially correlated; in other words, things that are close together tend to have similar characteristics.**

**It is important to understand that the interpolated values are approximations only of the real values of the surface and that the interpolated values differ depending upon the interpolation method used.**

Why interpolate?

**Visiting every location in a study area to measure the height, magnitude, or concentration of a phenomenon is usually difficult or expensive. Instead, dispersed sample input point locations can be selected and a predicted value can be assigned to all other locations. Input points can be either randomly, strategically, or regularly spaced points containing height, concentration, or magnitude measurements.**

**A typical use for point interpolation**

**is to create an elevation surface from a set of sample measurements. Each point represents a location where the elevation has been measured. The values between these input points are predicted by interpolation.**

**There are effectively two types of techniques for generating raster surfaces**

**Deterministic Models use a mathematical function to predict unknown values and result in hard classification of the value of features.**

**GeoStatistical Techniques**

**produce confidence limits to the accuracy of a prediction but are more difficult to execute since more parameters need to be set.**

**Deterministic Models**

**Deterministic models include Inverse Distance Weighted (IDW), Rectangular, Natural Neighbours, and Spline. You can also develop a trend surface using polynomial functions to create a customized and highly accurate surface.**

##
1Inverse Distance Weighting (IDW)

**The IDW technique calculates a value
for each grid node by examining surrounding data points that lie within a
user-defined search radius. The node value is calculated by averaging the
weighted sum of all the points. A radius is generated around each grid node
from which data points are selected to be used in the calculation.**
Options to control the use
of IDW include
Ø **Power**** a high power more emphasis is placed
on the nearest points and the resulting surface will have more detail and be
less smoothed. Its values range between one and ten.**
Ø **Search Radius ****defines the maximum size, in
map units, of a circular zone centered on each grid node within which point
values from the original data set are averaged and weighted according to their
distance from the node.**

**The IDW is usually
applied to highly variable data not desirable to local high/low values but
rather to look at a moving average of nearby data points and estimate the local
trends.**

2**Natural
Neighbourhood Interpolation**

**It is like IDW
interpolation, except that the data points used to interpolate the surface
values for each cell are identified and weighted using a Delaunay
triangulation.****The method thereby allows the
creation of accurate surface models from data sets that are very sparsely
distributed or very linear in spatial distribution.**

**Spline estimates values using a mathematical function that minimizes overall surface curvature, resulting in a smooth surface that passes exactly through the input points.****This method is best for gently varying surfaces, such as elevation, water table heights, or pollution concentrations. There are two spline methods…**

3**Spline
Interpolation**

**Spline estimates values using a mathematical function
that minimizes overall surface curvature, resulting in a smooth surface that
passes exactly through the input points.**

**This method is best for gently
varying surfaces, such as elevation, water table heights, or pollution
concentrations. There are two spline methods…**

**Spline
the Regularized Method**
**The
regularized method creates a smooth, gradually changing surface with values
that may lie outside the sample data range.**
**Spline
the Tension Method**

**It
creates a less-smooth surface with values more closely constrained by the
sample data range. For Tension, the higher the weight the coarser the generated
surface. The values entered have to equal or greater than zero. The typical
values are 0, 1, 5, and 10.**

4**Trend ****Interpolation**

**Trend
surfaces are good for identifying coarse scale patterns in data; the
interpolated surface rarely passes through the sample points.**
**Modelers
often work to the "fifth order" polynomial analysis.**

**The IDW technique calculates a value for each grid node by examining surrounding data points that lie within a user-defined search radius. The node value is calculated by averaging the weighted sum of all the points. A radius is generated around each grid node from which data points are selected to be used in the calculation.**

**Power**

**a high power more emphasis is placed on the nearest points and the resulting surface will have more detail and be less smoothed. Its values range between one and ten.**

**Search Radius**

**defines the maximum size, in map units, of a circular zone centered on each grid node within which point values from the original data set are averaged and weighted according to their distance from the node.**

**The IDW is usually applied to highly variable data not desirable to local high/low values but rather to look at a moving average of nearby data points and estimate the local trends.**

**Natural Neighbourhood Interpolation**

**Spline estimates values using a mathematical function that minimizes overall surface curvature, resulting in a smooth surface that passes exactly through the input points.**

**This method is best for gently varying surfaces, such as elevation, water table heights, or pollution concentrations. There are two spline methods…**

**Spline the Regularized Method**

**The regularized method creates a smooth, gradually changing surface with values that may lie outside the sample data range.**

**Spline the Tension Method**

**It creates a less-smooth surface with values more closely constrained by the sample data range. For Tension, the higher the weight the coarser the generated surface. The values entered have to equal or greater than zero. The typical values are 0, 1, 5, and 10.**

**Trend surfaces are good for identifying coarse scale patterns in data; the interpolated surface rarely passes through the sample points.**

**Modelers often work to the "fifth order" polynomial analysis.**