# Comparison of Spatial Interpolation Methods: Cross Validation, RMS Error, Validation (Especially for GATE-Geospatial 2022)

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Using same data with different interpolation methods, one can find different interpolation results. Likewise, different predicted values can occur by using the spatial interpolation method.

Comparison of local methods is usually based on statistical measures, although some studies have also suggested the importance of the visual quality of generated surfaces such as preservation of distinct spatial pattern and visual pleasantness and faithfulness.

How can different interpolation methods compared?

• Local methods are usually compared on the base of statistical measures.
• Visual quality of predicted surface.
• Cross validation is a common technique for comparison

## Cross Validation

Consider each point as unknown point and predict that point then compare the value of known point with the predicted value of the same point.

Or create subset of original data and predict the values for subset using known point and compare the predicted values with known points.

## Cross Validation Procedure

Cross-validation compares the interpolation methods by repeating the following procedure for each interpolation method to be compared:

1. Remove a known point form the data set.

2. Use the remaining points to estimate the value at the point previously removed.

3. Calculate the predicated error of the estimation by comparing the estimated with the known value.

when root mean square in mean action and means estimation.

## Standardized RMS Error

Standardized RMS Error

A better interpolation method should produce a smaller RMS error.

A better kriging method should produce a smaller RMS error and a standardize RMS close to 1.

## Validation Techniques

This technique compares the interpolation methods by 1st dividing known points into two samples.

• One sample for developing the model for interpolation
• Other sample for testing the accuracy of the model

The statistics RMS error and standardize RMS error derived from the test sample can then be used to compare the method.

Validation may not be a feasible option if the number of known points is too small to be split into two samples.

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