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

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.

Modern Development for the Improvement of Accuracy of Nigerian Coordinate Transformation Process Using the Adapted NTv2 Model: The Critical Issues of the Mathematical Algorithm

Changing coordinates using appropriate mathematical models from one reference system to another may be influenced if the operation requires the change of datum. A set of transformation parameters has been adopted for Nigeria. However, the critical concern usually associated with the problem of transformation of coordinates is the issue of recoverability of the original values of transformed coordinates. The recursive effect of variables associated with spatial problems can be aptly modelled with an appropriate algorithm that set out a process to achieve a definite output. Consequently, the main thrust of this paper is to highlight the critical elements of the mathematical algorithm associated with the National Transformation Version 2 (NTv2) model adapted for the Nigerian Datum Transformation process. The adapted NTv2 model adopts the bi-linear interpolation approach and the covariance function obtained were used to generate transformation elements in latitude (Δφp) and longitude (Δλp) and corresponding accuracies at the lattice nodes. The mathematical algorithm of this adapted NTv2 model underscores the likely attainment of better and significant values and statistical indicator of the improved accuracy as the average shift values for latitude and longitude for any transformed points in Nigeria. This capability makes the mathematical algorithm to be adaptable and fit for the purpose of the transformation process. The improvement in the positional accuracy is directly attributable to the application of the NTv2 model which provides a flexible and robust system of modelling any inherent systematic error in the national network.