Improved Kriging Algorithms for Spatial Data Interpolation

Abstract

Landscape visualization is important in environmental planning. Environmental planners need accurate spatially continuous data across an area to make competent and confident decisions. Obtaining such information can be difficult and costly, particularly in mountainous or deep-sea regions. In addition, environmental data gathered from field surveys are frequently derived from point sources. To generate spatially continuous data, the values of an attribute at unsampled points must therefore be estimated. In such cases, spatial interpolation techniques can be employed to predict the height values at unsampled sites using data from point observations. In this thesis, we propose three novel algorithms for spatial interpolation methods using kriging models. Since there are not many findings of how kriging parameters in the semivariance model affect the performance of the spatial interpolators, we explore the parameters of the kriging algorithm and propose different semivariogram models to improve the performance of the spatial interpolation technique. Our three new models are compared with five contemporary kriging models. The performance is evaluated by error reduction that eight models can perform. The strengths of each model are analyzed based on a different set of sample sizes coming from two zones of study areas. The resulting errors of our proposed methods are relatively small. The lower bounds of the 95% confidence interval of our models are mostly lower than all five contemporary models. However, in general, the result shows no much significant differences among models. The benefits of this work are that it contributes to better accuracy resulting in more reliable decision making; supports different needs of algorithms for different area types, and can be practically used to improves the 3D surface plot in environmental planning. Although our three new algorithms are accurate approaches, we found that applying them for landscape 3D visual assessment is not so practical as the waiting time to complete the model surface plot can be up to 5 days. Therefore, the second challenge is to reduce the computational time to be less than 5 minutes while preserving the accuracy or reducing it down marginally. The thesis presents two additional algorithms by first applying the divide and conquer technique and later improving it by introducing a slope (terrain variation) threshold parameter. The final result reduces the waiting time further down to 4 minutes.