Accuracy Assessment and Comparative Analysis of IDW, Spline and Kriging in Spatial Interpolation of Landform (Topography): An Experimental Study

Maduako Nnamdi Ikechukwu,Ndukwu Ike Raphael,Elijah Ebinne,Ufot Idorenyin

doi:10.4236/jgis.2017.93022

Maduako Nnamdi Ikechukwu, Ndukwu Ike Raphael + Show 2 more

Open Access

https://doi.org/10.4236/jgis.2017.93022

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Abstract

It is practically impossible and unnecessary to obtain spatial-temporal information of any given continuous phenomenon at every point within a given geographic area. The most practical approach has always been to obtain information about the phenomenon as in many sample points as possible within the given geographic area and estimate the values of the unobserved points from the values of the observed points through spatial interpolation. However, it is important that users understand that different interpolation methods have their strength and weaknesses on different datasets. It is not correct to generalize that a given interpolation method (e.g. Kriging, Inverse Distance Weighting (IDW), Spline etc.) does better than the other without taking into cognizance, the type and nature of the dataset and phenomenon involved. In this paper, we theoretically, mathematically and experimentally evaluate the performance of Kriging, IDW and Spline interpolation methods respectively in estimating unobserved elevation values and modeling landform. This paper undertakes a comparative analysis based on the prediction mean error, prediction root mean square error and cross validation outputs of these interpolation methods. Experimental results for each of the method on both biased and normalized data show that Spline provided a better and more accurate interpolation within the sample space than the IDW and Kriging methods. The choice of an interpolation method should be phenomenon and data set structure dependent.

Highlights

Interpolation aims at finding the values of a function f ( x) for an x between different x values x0, x1, xn at which the values of f ( x) are given
It is not correct to generalize that a given interpolation method (e.g. Kriging, Inverse Distance Weighting (IDW), Spline etc.) does better than the other without taking into cognizance, the type and nature of the dataset and phenomenon involved
Unlike the IDW methods, the values predicted by Radial Basis Functions (RBF) are not constrained to the range of measured values, i.e., predicted values can be above the maximum or below the minimum measured value [14]

Summary

Introduction

Interpolation aims at finding the values of a function f ( x) for an x between different x values x0 , x1, , xn at which the values of f ( x) are given. Interpolation becomes very useful and essential in scenarios where, the resolution, orientation, or cell size of a discretized surface varies from what is needed It is employed when continuous surface is represented by a data model different from what is desired, and when data spread does not cover an area of interest totally [3]. The relationship between target variable and the physical environment cannot be modeled exactly because of its complexity [5]. This is due to a lack of sufficient knowledge of: (a) the complete list of inputs into the model (b) the relationship needed to determine the output from these inputs and (c) the importance of the random part of the system. Estimating a model using field measurement of the parameter of interest becomes the only way [6]

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