Spatial Interpolation Techniques

Interpolation is used for prediction of values in a raster format, using a limited number of available sample data. The interpolation can be done using ground observation of any of parameter of interest like elevation, rainfall, N P K values in agriculture etc. The GIS softwares provide the capability to convert the ground data into points, provided the ground data has lat long values in it. Once ground observations are converted into points, we can use any of suitable interpolation method.

According to ESRI, “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, such as elevation, rainfall, chemical concentrations, and noise levels.”

Fig: IDW Interpolation for nitrogen data

Why interpolate to raster?

The assumption that makes interpolation a viable option is that spatially distributed objects are spatially correlated; in other words, things that are close together tend to have similar characteristics. For instance, if it is raining on one side of the street, you can predict with a high level of confidence that it is raining on the other side of the street. You would be less certain if it was raining across town and less confident still about the state of the weather in the next county.

Using the above analogy, it is easy to see that the values of points close to sampled points are more likely to be similar than those that are farther apart. This is the basis of interpolation. A typical use for point interpolation is to create an elevation surface from a set of sample measurements. Geostatistical Analyst also provides and extensive collection of interpolation methods.

(Geostatistical Analyst Tutorial link is given below)

There are many interpolation techniques available i.e. Kriging, IDW, Natural neighbour, Spline, Spline with barriers, Topo to ratser, Trend, etc. The GIS arena giant ESRI has provided short and very relevant definitions to all these interpolation techniques which are available in ArcGIS software. The definitions are given below-

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.

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.

Natural neighbour

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.

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.

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.

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.

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.

Kriging vs. IDW

IDW has more simple procedure and fewer steps compared to Kriging. The advantage of IDW is that it is intuitive and efficient hence recommended for less informative type of data.

However, for more informative data, Kriging is more preferable. Indeed, Kriging provides a more reliable interpolation because it examines specific sample points to obtain a value for spatial autocorrelation that is only used for estimating around that particular point, rather than assigning a universal distance power value.

Furthermore, Kriging allows for interpolated cells to exceed the boundaries of the sample range.

Figure Courtesy: Setianto and Triandini, 2013

References:

[1] Understanding Interpolation Analysis, ESRI.

http://pro.arcgis.com/en/pro-app/tool-reference/3d-analyst/understanding- interpolation-analysis.htm

[2] Comparing Interpolation Methods, ESRI.

http://pro.arcgis.com/en/pro-app/tool-reference/3d-analyst/comparing-

interpolation-methods.htm

[3] Agung Setianto and Tamia Triandini, 2013, Comparison of Kriging And

Inverse Distance Weighted (IDW) Interpolation Methods in Lineament

Extraction and Analysis. J. SE Asian Appl. Geol., 2013, Vol. 5(1), pp. 21–29

[4] Parikshit Ranade, Dr Ayse Irmak and David R. Maidment, 2008,

Geostatistical Analyst,

https://www.caee.utexas.edu/prof/maidment/giswr2008/geostat/ExGeostat.doc

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