Spatial Sampling Strategies for the Effect of Interpolation Accuracy

Hairong Zhang,Wei Liu,Lijiang Lu,Yanhua Liu

doi:10.3390/ijgi4042742

Abstract

Spatial interpolation methods are widely used in various fields and have been studied by several scholars with one or a few specific sampling datasets that do not reflect the complexity of the spatial characteristics and lead to conclusions that cannot be widely applied. In this paper, three factors that affect the accuracy of interpolation have been considered, i.e., sampling density, sampling mode, and sampling location. We studied the inverse distance weighted (IDW), regular spline (RS), and ordinary kriging (OK) interpolation methods using 162 DEM datasets considering six sampling densities, nine terrain complexities, and three sampling modes. The experimental results show that, in selective sampling and combined sampling, the maximum absolute errors of interpolation methods rapidly increase and the estimated values are overestimated. In regular-grid sampling, the RS method has the highest interpolation accuracy, and IDW has the lowest interpolation accuracy. However, in both selective and combined sampling, the accuracy of the IDW method is significantly improved and the RS method performs worse. The OK method does not significantly change between the three sampling modes. The following conclusion can be obtained from the above analysis: the combined sampling mode is recommended for sampling, and more sampling points should be added in the ridges, valleys, and other complex terrain. The IDW method should not be used in the regular-grid sampling mode, but it has good performance in the selective sampling mode and combined sampling mode. However, the RS method shows the opposite phenomenon. The sampling dataset should be analyzed before using the OK method, which can select suitable models based on the analysis results of the sampling dataset.

Highlights

Spatial interpolation is the procedure of deriving the characteristic values of unknown data at specified points and the characteristics of data distribution based on the known data at specific points in the same area, which plays a significant role in spatial analysis [1].More than twenty spatial interpolation methods have been used in different fields
Liu et al analyzed the spatial variability of elevation, and the results showed that the ordinary kriging (OK) method was the best interpolation method [9]
The accuracy of the interpolation results of the three methods is analyzed with respect to four characteristics: the distribution of errors, maximum absolute errors (MAX), bias of errors (BIAS), and root mean squared of errors (RMSE)

Summary

Introduction

Spatial interpolation is the procedure of deriving the characteristic values of unknown data at specified points and the characteristics of data distribution based on the known data at specific points in the same area, which plays a significant role in spatial analysis [1]. More than twenty spatial interpolation methods have been used in different fields. According to the mathematical mechanism of interpolation, these interpolation methods can be classified as non-geostatistical methods and geostatistical methods. Non-geostatistical methods include the nearest neighbor method, inverse distance weighted method, local polynomial method, and regular spline method. The kriging method is the most common geostatistical method. Each interpolation method has different factors that affect the interpolation accuracy, and all affecting factors should be considered when interpolation methods are used. The variance and variograms should be analyzed before using the kriging interpolation method

Methods

Results

Discussion

Conclusion