Performance Comparison of Covariance Function to Interpolate Unsampled Points with Simulation Data in Manado City

Abstract

The covariance function measures the strength of statistical correlation as a function of distance. This follows Tobler's law which states that everything is usually related to all else but those which are near to each other are more related when compared to those that are further away. The correct weight of the basic covariance structure will produce the optimal kriging predictor. One interesting way to evaluate the strength of a kriging interpolation is to perform a simulation using a spatial structure. The simulation technique is executed in Manado City. The data is then applied to the variogram model using the spherical and matern covariance functions. The type of kriging method used in this simulation is ordinary kriging. The result shows that the suitable model to use is the matern model. Residual results from cross-validation show that the matern model has a lower biased estimation on both data. According to the RMSE and MAE criteria, the matern model outperforms the spherical model on data A and data B. The results of the interpolation are then visualized in the form of a map. Through this research, it can be concluded that the accuracy of the selection of the covariance function in the variogram model will provide a good estimate for the kriging method, and the most appropriate model for this case is the matern model.