Available online at http://iorajournal.org/indx.php/orics /index Operations Research: International Conference Series Vol. 3, No. 3, pp. 118-126, 2022 e-ISSN: 2722-0974 p-ISSN: 2723-1739 Performance Comparison of Covariance Function to Interpolate Unsampled Points with Simulation Data in Manado City Claudya Soleman 1* Winsy Weku 2 , Deiby Salaki 3 1,2,3 Departement of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Sam Ratulangi, Manado, Indonesia *Corresponding author winsy_weku@unsrat.ac.id 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. Keywords: Covariance function, interpolation, simulation data 1. Introduction Covariance modeling plays a key role in spatial data analysis because it provides information about the dependency structure of the underlying processes and determines the performance of spatial predictions. Various parametric models have been developed to accommodate the idiosyncratic features of a given dataset. However, parametric models can impose unjustified restrictions on the covariance structure and the procedure for selecting a particular model is often ad-hoc (Choi, 2014). Covariance measures the assumption that things that are close tend to be more similar than things that are far apart. Covariance measures the strength of statistical correlation as a function of distance. The process of modeling the covariance function adjusts the curve to the available empirical data. It aims to reach the most suitable model which will then be used in the predictions (Esri, 2021). The correct weight of the basic covariance structure will produce the optimal kriging predictor. An important, but not well-understood issue in kriging theory is the effect on the accuracy of the kriging predictor in substituting optimal weights for weights derived from the estimated covariance structure. In practice, the structure of this covariance is unknown and estimated from the data (Putter, 2021). A comparison of the kriging interpolation variance model has been studied by (Marko, 2013) regarding the spatial distribution of groundwater quality, and the prediction of groundwater chemical parameters was carried out using geostatistical analysis on Geographic Information System (GIS) software using the Ordinary Kriging method. The best model for each parameter was assessed based on the root mean square error (RMSE) criteria. Rozalia et al. (2016) (Rozalia, 2014) have also researched estimating NO2 levels in the air in the city of Semarang using the Ordinary Kriging method, which then made a comparison between several variance models, namely spherical, exponential, and gaussian to get the best model to be used in the estimation. Based on this analysis, it was found that the best model is the spherical model which produces the highest estimation of Nitrogen Dioxide in Sub Gebangsari and the lowest Nitrogen Dioxide in Sub Patemon. (Sophal, 2014) is also one of the groups that examine the spatial distribution of soil