Prediction of geoid undulations: Random forest versus classic interpolation techniques

Abstract

Local geoid determination studies are commonly carried out today to establish the relationship between the ellipsoidal height (h)$$ (h) $$ determined by satellite geodesy methods and the orthometric height (H)$$ (H) $$ found using geoid undulation (N)$$ (N) $$. The aim of this study was to determine a local geoid using the kriging, local polynomial (LP), and inverse distance to a power (IDP) interpolation methods along with the random forest (RF) regression method and to compare the performance. For the application, 193 Global Navigation Satellite System (GNSS)/leveling points homogeneously distributed over the study area were selected as reference data, and 70 GNSS/leveling points were selected as test data. The results were compared in terms of accuracy using well-known performance metrics, namely, the root mean square error (RMSE), mean absolute error (MAE), and coefficient of determination (R-2) values. According to the results, the highest R-2 and the lowest RMSE and MAE values were obtained with the RF regression method. These findings demonstrated the superiority of the RF regression over the classic interpolation methods applied in the local geoid determination for the study area.