Spatial uncertainty of a geoid undulation model in Guayaquil, Ecuador

Abstract

Geostatistics is a discipline that deals with the statistical analysis of regionalized variables. In this case study, geostatistics is used to estimate geoid undulation in the rural area of Guayaquil town in Ecuador. The geostatistical approach was chosen because the estimation error of prediction map is getting. Open source statistical software R and mainly geoR, gstat and RGeostats libraries were used. Exploratory data analysis (EDA), trend and structural analysis were carried out. An automatic model fitting by Iterative Least Squares and other fitting procedures were employed to fit the variogram. Finally, Kriging using gravity anomaly of Bouguer as external drift and Universal Kriging were used to get a detailed map of geoid undulation. The estimation uncertainty was reached in the interval [-0.5; +0.5] m for errors and a maximum estimation standard deviation of 2 mm in relation with the method of interpolation applied. The error distribution of the geoid undulation map obtained in this study provides a better result than Earth gravitational models publicly available for the study area according the comparison with independent validation points. The main goal of this paper is to confirm the feasibility to use geoid undulations from Global Navigation Satellite Systems and leveling field measurements and geostatistical techniques methods in order to use them in high-accuracy engineering projects.

Keywords

• ellipsoidal height
• stationarity
• anisotropy
• trend