What is Interpolation?

Interpolation

In the mathematical field of numerical analysis, interpolation is a method of constructing new data points within the range of a discrete set of known data points.

Interpolation is a Geo statistical term. It means to fill up missing values estimate missing or example values by using knowing or sampled values with statistical and mathematical models, linear.

On the map the digitize is called spatial interpolation. Between two missing values to fill them is called interpolation.

Types of Interpolation:

There are six major types of interpolation

Ø  Exact Interpolation:

The exact interpolation is one in which the surface line passes through the sampled points.

Ø  Inexact Interpolation:

Inexact interpolation is one in which the surface line passes near to the sampled.

Ø  Deterministic:

Deterministic interpolation creates surface from measured points based on either extent of               similarity or degree of smoothing. Errors cannot be measured in deterministic interpolation.

Ø  Stochastic Interpolation:

Stochastic interpolation is a statistical based interpolation. It creates surface measured points and can measure errors.

Ø  Global Interpolation:

In global interpolation we may take all points in given area. To construct interpolation

Ø  Local Interpolation:

In global interpolation only specific points in assign location are used to create interpolation surface.

Method of Interpolation:

There are many methods of interpolation we will describe four major methods of interpolation.

Ø  IDW:

The IDW (Inverse Distance Weighted) tool uses a method of interpolation that estimates cell values by averaging the values of sample data points in the neighborhood of each processing cell. The closer a point is to the center of the cell being estimated, the more influence, or weight, it has in the averaging process.

Ø  Kriging:

Kriging is an advanced geostatistical procedure that generates an estimated surface from a scattered set of points with z-values. More so than other interpolation methods, a thorough investigation of the spatial behavior of the phenomenon represented by the z-values should be done before you select the best estimation method for generating the output surface.

Ø  Natural Neighbor:

Natural Neighbor interpolation finds the closest subset of input samples to a query point and applies weights to them based on proportionate areas to interpolate a value (Sibson, 1981). It is also known as Sibson or "area-stealing" interpolation.

Ø  Spline:

The Spline tool uses an interpolation method that estimates values using a mathematical function that minimizes overall surface curvature, resulting in a smooth surface that passes exactly through the input points.

Ø  Spline with Barriers:

The Spline with Barriers tool uses a method similar to the technique used in the Spline tool, with the major difference being that this tool honors discontinuities encoded in both the input barriers and the input point data.

Ø  Topo to Raster:

The Topo to Raster and Topo to Raster by File tools use an interpolation technique specifically designed to create a surface that more closely represents a natural drainage surface and better preserves both ridgelines and stream networks from input contour data.

The algorithm used is based on that of ANUDEM, developed by Hutchinson et al at the Australian National University.

Ø  Trend:

Trend is a global polynomial interpolation that fits a smooth surface defined by a mathematical function (a polynomial) to the input sample points. The trend surface changes gradually and captures coarse-scale patterns in the data.

Ø  Linear Interpolation Method:

Linear interpolation is the simplest method of getting values at position in between the data points. The points are simply joined by straight line segments. Each segment (bounded by two data points) can be interpolated independently.

The parameter mu defines where to estimate the value on the interpolated line, it is 0 at the first point and 1 and the second point.

Digital Elevation Model:

Digital elevation model is a raster data set provides 3D dimensional information of earth surface. Different function can be applied digital elevation model through spatial analyst toolbar, contour, slope, aspect Hill/ shade.